There are four tracks, plasmids, engineering tonics, combat tonics, and physical tonics. Each track has six slots that you can fill up. Two are available right away, but you have to purchase the others at a Gatherer’s Garden. Maxing out one of the four tracks gets you this trophy.

There are four tracks, plasmids, engineering tonics, combat tonics, and physical tonics. Each track has six slots that you can fill up. Two are available right away, but you have to purchase the others at a Gatherer’s Garden. Maxing out all four of the tracks gets you this trophy.

Buy one slot in either the plasmid, engineering tonic, combat tonic, or physical tonic at any Gatherer’s Garden location.

Upgrade one of your guns, the pistol, shotgun, machine gun, chemical thrower, grenade launcher, or the crossbow. There are two upgrades available for each gun, so getting one upgrade for any of them will give you this trophy. The most likely point you’ll get this is at the end of the Neptune’s Bounty level. After the fight with Peach Wilkins, you’ll have to find the submarine bay. On the way to this, there will be a Power to the People station where you can upgrade a weapon.

Purchase both upgrades for any one of the guns in the game, the pistol, the shotgun, the machine gun, the chemical thrower, the grenade launcher, or the crossbow.

Purchase both upgrades for any two of the guns in the game, the pistol, the shotgun, the machine gun, the chemical thrower, the grenade launcher, or the crossbow.

Purchase both upgrades for any three of the guns in the game, the pistol, the shotgun, the machine gun, the chemical thrower, the grenade launcher, or the crossbow.

Purchase both upgrades for any four of the guns in the game, the pistol, the shotgun, the machine gun, the chemical thrower, the grenade launcher, or the crossbow.

Purchase both upgrades for any five of the guns in the game, the pistol, the shotgun, the machine gun, the chemical thrower, the grenade launcher, or the crossbow.

Purchase both upgrades for all of the guns in the game, the pistol, the shotgun, the machine gun, the chemical thrower, the grenade launcher, or the crossbow. There are 12 stations in all, and here are the locations of the Power to the People stations (thanks to Little_Moth at Gamefaqs for this):

Completely finish all five levels of research for the Thuggish Splicer. These splicers are the ones with lead pipes and try to melee attack you. Take lots of pictures of them to get through the levels. Higher grade photos give you more points. You can take multiple photos per splicer, but the grade of each subsequent photo drops. You get a maximum of three or four photos per splicer.

Completely finish all five levels of research for the Leadhead Splicer. These splicers are the ones with pistols or machine guns. Take lots of pictures of them to get through the levels. Higher grade photos give you more points. You can take multiple photos per splicer, but the grade of each subsequent photo drops. You get a maximum of three or four photos per splicer.

Completely finish all five levels of research for the Spider Splicer. These splicers are the ones that climb on ceilings and walls, throw hooks at you, and jump or cartwheel everywhere. Take lots of pictures of them to get through the levels. Higher grade photos give you more points. You can take multiple photos per splicer, but the grade of each subsequent photo drops. You get a maximum of three or four photos per splicer.

Completely finish all five levels of research for the Houdini Splicer. These splicers are the ones that teleport their way around. They mostly use fire or ice plasmids to attack you. Take lots of pictures of them to get through the levels. Higher grade photos give you more points. You can take multiple photos per splicer, but the grade of each subsequent photo drops. You get a maximum of three or four photos per splicer.

Completely finish all five levels of research for the Nitro Splicer. These splicers are the ones that throw grenades at you and carry around boxes of grenades. Take lots of pictures of them to get through the levels. Higher grade photos give you more points. You can take multiple photos per splicer, but the grade of each subsequent photo drops. You get a maximum of three or four photos per splicer.

Completely finish all five levels of research for the Rosie. These Big Daddies have the one light on their heads and are the ones with rivet guns. Take lots of pictures of them to get through the levels. Higher grade photos give you more points. You can take multiple photos per Big Daddy, but the grade of each subsequent photo drops. You get a maximum of three or four photos per Big Daddy.

Completely finish all five levels of research for the Bouncer. These Big Daddies have multiple lights on their heads and have a drill on one of their hands. Take lots of pictures of them to get through the levels. Higher grade photos give you more points. You can take multiple photos per Big Daddy, but the grade of each subsequent photo drops. You get a maximum of three or four photos per Big Daddy.

Completely finish all five levels of research for the Little Sister. These are the little girls that walk around with the Big Daddies. Take lots of pictures of them to get through the levels. Higher grade photos give you more points. You can take multiple photos per Little Sister, but the grade of each subsequent photo drops. You get a maximum of three or four photos per Little Sister.

To do this, you have to take one picture of each of each type of enemy. These enemies are Thug Splicer, Leadhead Splicer, Spider Splicer, Houdini Splicer, Nitro Splicer, Roise, Bouncer, Little Sister, Turret, Security Bot, and Security Camera.

Finish all five levels of research for all the splicers, both Big Daddies, the Little Sister, as well as the security camera, the security bots, and the turrets.

You have to take a picture of a splicer that gets an A grade. Getting certain things, such as multiple splicers or an action shot (jumping up or attacking you) of the splicer, in the picture up the grade of the photo. Make sure the photo is centered on the splicer, the splicer is pretty clear, and is completely (or mostly) in the picture.

As soon as you get the camera in Neptune’s Bounty, there will be a splicer in the next room. Take a picture of it through the glass, and this trophy will be yours.

Hack either a security bot, a security camera, a turret, a vending machine, or a safe. The first place you’ll be able to do this is in the Medical Pavilion. There will be a security bot that is stuck in the opening of a door at the beginning of the level. If you're facing the vending machine, it's to the right of it. These are mini-games with a time limit where you have to uncover squares and construct a pipe from one point to another while fluid is flowing through the pipe. The earlier you can get these in the game, the better since the hacks will be easier. Saving before attempting the hack is a good idea since you can reload it if you fail.

Hack any of the security bots that are littered throughout the game. A good place to do this is at the beginning of the Medical Pavilion. There will be a security bot that is stuck in the opening of a door at the beginning of the level. If you're facing the vending machine, it's to the right of it.

Hack any security camera around Rapture. In the Medical Pavilion, there are a couple of security cameras that are easy to hack. The one you'll most likely encounter first is in the Eternal Flame crematorium. Get beneath the camera without being spotted (stay out of the pink light), and look up to start the hack.

Hack any turret that is in Rapture. There are few turrets in the Medical Pavilion that you can hack. There will be two in the large room after the entrance to the Medical Pavilion (where you see the ghost at the door). Hit one with Electro Bolt, then go up to it and hack it.

Hack any vending machine that you find. There are two types of vending machines, the Circus of Value and the El Ammo Bandito. Both of those are found in the Medical Pavilion. Off to the side of the large room where you first see turrets, there is a room with both types of vending machines. Hack either one.

Hack any of the safes found in Rapture. Safes are usually hidden or out of the way and are few and far between. These are usually the toughest of the machines to hack. There is one in the Twilight Fields Funeral Home in the Medical Pavilion. To get in there, you'll need to have Incinerate to melt the ice. When you go in, it's on the left side. You'll get attacked by a splicer and then a turret. If you haven't hacked a turret already, now would be a good time because the safe is behind the turret.

Hack any combination of 50 turrets, security camera, security bots, safes, vending machines, health stations, or U-Invents. Using buyouts and auto hack tools also count towards this trophy and all other hacking trophies.

Invent one item at a U-Invent. You can invent three tonics (Hacker’s Delight 2, Bloodlust, and Booze Hound), the automatic hacking tool, and six ammo types (antipersonal pistol rounds, armor-piercing machine gun rounds, exploding buck, heat-seeking RPG, electric gel, and trap bolts). The items for these start to appear in the “Arcadia” level.

Invent any combination of 100 tonics, ammo types, or automatic hacking tools at U-Invent stations in Rapture.

Invent one each of the six ammo types, antipersonal pistol rounds, armor-piercing machine gun rounds, exploding buck, heat-seeking RPG, electric gel, and trap bolts at U-Invent stations.

This trophy is tough for some people. There are tonics scattered around Rapture. If you’re searching for the audio diaries, you should be able to find these pretty easily. Others can be purchased from any Gatherer’s Garden. Rescuing Little Sisters gives you more Adam to work with and allows you to purchase more tonics. Taking research photos and maxing out all research also gives you some plasmids. Don't purchase all the upgrades to your Health and Eve. If you do, you won't have enough Adam to buy all the tonics for this trophy. There are a total of 58 tonics in Rapture, so you have to find all of them. 
PerpetualHeaven wrote a good guide detailing how to get every tonic. Here is the link to that: Dairy, Tonic, and Weapon Upgrade Guide With Maps - PS3Trophies.org

Finish the game on Hard. If you play through on Survivor, and not Hard, you’ll unlock all the difficulty trophies as long as you don’t use a Vita-Chamber.

Every stage beginning with the “Medical Pavilion” has at least one Big Daddy and Little Sister. Most have two or three. The easiest way to deal with the Big Daddies is to hit them with Electrobolt or Electric Buck shells to stun them, and fire away. Harvesting each Little Sister gives you a lot of Adam right then, but if you rescue them, you’ll get less at the moment, but you’ll get more in the long run and some tonics from Dr. Tenenbaum.

At the beginning of Fort Frolic, you’ll come across some slot machines. Play until you hit a jackpot. This is random and based on luck. Save right before you use the slots, then play the slots until you get the trophy (reload your save if you run out of money), and once you have the trophy, reload your save so don’t lose any money (unless you end up with more than you started with).

Use the Electrobolt plasmid on a splicer that is standing in water. A good place for this is in “Welcome to Rapture.” In the area with the first audio diary, go down the stairs, and there will be a couple of splicers in a room that is filled with water. Fire Electrobolt at them, and the trophy is yours.

There are 122 audio diaries that are scattered throughout Rapture. This site has maps and the locations of all 122 audio diaries:

Visual Walkthroughs - BioShock Walkthrough - BioShock Maps  

• Please note that the two audio diaries in “Welcome to Rapture” CANNOT be gone back to. If you miss those two, you can’t get this trophy.
• There are three missable ones in Rapture Central Control. One is on a desk to the left of the entrance in a room with a lot of pictures and words on the walls (thanks to Cauchy-Schawrz for the reminder). There are also two audio diaries in the Rapture Core where you go golfing with Andrew Ryan. If you miss these three, you CANNOT go back for them.
• All of the other ones you can go back to in the Bathyspheres up to just before the last fight.

Finish the game on Hard, but switch Vita-Chambers to “Off” in the Options menu. If you play through on Survivor, and not Hard, you’ll unlock all the difficulty trophies as long as you don’t use a Vita-Chamber.

Finish the game on Survivor. Completing the game on Survivor will also unlock the trophies for Hard, as long as you don’t use a Vita-Chamber.

Finish the game on Survivor. Switch Vita-Chambers to “Off” in the Options menu. Completing the game on Survivor will also unlock the trophies for Hard, as long as you don’t use a Vita-Chamber. Some tips:

1. Save a lot. Save after every major fight. Save as often as you can.
2. DO NOT play another game save that is set to another difficulty. Doing this may not get you the trophy.
3. Take lots of pictures. Take pictures of everything.
4. Search everywhere for items. Take as much ammo and all the items you can carry.
5. Rescuing the Little Sisters gets you more Adam, which gets you more tonics and plasmids to use. Rescue all of them.

Unlock all of the bronze, silver, and gold trophies and it's yours. 

NOTE: You don't need to complete the challenge room downloadable content to get the platinum trophy, but you will need to complete them if you want to have a 100% on your PSN profile.

Rescue the Little Sister in this challenge room. These rooms are puzzles and take a bit of thought to work out what to do. This is the first of the three rooms. You have to recuse the Little Sister from a Big Daddy that has gone crazy, but you'll have an extremely limited selection of weapons. The only weapon that you'll find is the grenade launcher, and the plasmids that you have to work with are "Target Dummy" and "Winter Blast." You'll also need to find enough items to invent an Automatic Hacking Tool.

This is a speed run through this challenge room. It isn’t too difficult, but does take some practice. Follow this video:

There are four roses in this challenge. Follow this video for the locations:

This takes some thinking to work out how best to do it. Use Target Dummy to get the rocket turrets and machine gun turrets to fire, but keep the target far enough away from the machine gun turrets so they aren't destroyed. Then you have to make it through the explosions and gunfire without dying. Once you have the other door open, you have to kill the Big Daddy without destroying the turrets. If you need more info, follow this video:

Rescue the Little Sister in this challenge room. These rooms are puzzles and take a bit of thought to work out what to do. Again, you have limited equipment in this room. This room has a bit more combat then the previous room. The weapons that you have available are the crossbow (with a few trap bolts), the chemical thrower (with some electric gel), and the shotgun (with a electic buck...do you see a pattern here?). The only tonics that you have to use are Static Discharge and Expert Piano Player (yay?). Your goal is to rescue the Little Sister from the top of a Ferris Wheel that has shorted out. You'll have to turn the wheel six times to get her down and nine times to get "Master Electrician" and "Collector."

This is a speed run through this challenge room. It isn’t too difficult, but does take some practice. Follow this video:

There are 10 roses in this challenge. Follow this video for the locations:

Locations (Thanks to TheNukes, fords30, and Killerxx for the locations):
1. In one of 3 the barrels in one of the huts inside the big market room
2. Above you on the ceiling in the room with the code jump up and grab it (code 1951)
3. Inside Rapture Records behind the metal fence
4. Washrooms, Gents side on top of the Pick your Plasmid picture
5. Inside the Ice room above in the pipe below the Punemo
6. Inside the axle of the Ferris Wheel to the left of the lever, you must energize the wheel 7 times and the right one of the 2 axles will blow up revealing a rose inside. 
7. Inside the most bottom right balloon over in the market room balloon stand. You can either pop this with some ammo or have a splicer beat on you infront of the stand until it pops.
8. Inside the little sister vent. It's located on your right as you enter the carnival area.
9. On the 2nd floor in the main lobby, go to the lift shaft on the left and look up to your right. There's a gap with a corpse and a rose in. Jump to get it.
10. On Top of the Elevator when the lady push the button and get shocked get on the top of the elevator as it comes up

You have to find and save all of the different types of electric ammo that is in this challenge (electric buck, electric gel, & trap bolts). Stand next to the wheel controls and kill the splicers with Static Discharge (let them hit you). You'll have to get them to chase you to the controls. Follow this video if you need more info:

This challenge room is just a straight fight. There isn’t any puzzle to follow here, it’s just a fight through eight rooms to make the Little Sister feel safe enough that she'll come out of the chamber she trapped herself in. You have every weapon and a good selection of tonics/plasmids to work with. After you kill the splicer in the first room, "A Single Splicer," the Little Sister will give a gift with every weapon along with some money and Adam. How you spend the money and Adam on ammo, items, plasmids, and tonics is up to you. I would recommend spending the money an health packs, Eve hypos, and crossbow bolts. Make sure you pick up plenty of items (3 distilled water, 1 alcohol, 2 battery) to invent some electric gel for when you have to fight a room with four Big Daddies. 

You have four plasmid slots available to you. Three of these should be taken by Electrobolt, Incinerate, and Enrage. The fourth you can use for whatever tonic you want. The hacking tonic won't help you too much, so don't bother wasting Adam on them. The tonics that you should have (especially when going for "Tough Guy") are Photographer's Eye, Damage Research, Clever Inventor (this is a must if you plan on using Electric Gel), Armored Shell, Static Discharge, and Wrench Jockey.

This is the hardest trophy that you’ll encounter in the DLC. Getting under 15:00 is difficult, but can be done with a few practice rounds. A good order to do them in is: One Splicer, One Big Daddy, Flying Bots (finish those three in under 2:45), Turret Maze, Spider Splicers, Splicers Mix, Four Big Daddies (use Enrage! to get them fighting each other and then use everything you can on them), Houdini Splicers (finish all the rooms in under 13:00). The last room shouldn't take any more than 2:00. Go for headshots with the crossbow for quick kills.

There are numerous threads that have more tips if you need them. This is the thread that I used: World of Hurt - Expert - PS3Trophies.org
Thank you to Metapower for the recommended order of the rooms.

There are eight roses in this challenge, one in each room. Follow this video for the locations:

This trophy is surprisingly easy. Equip as many tonics and plasmids like Electrobolt, Incinerate, and Enrage. Max out the research with the camera and take your time in these rooms. Make sure you have Photographer's Eye, Damage Research, Armored Shell, Static Discharge, and Wrench Jockey as your equipped tonics. The room with the Big Daddies will be the toughest. Using Enrage, Incinerate, and Electrobolt on the Big Daddies while they fight each other is the easiest way to do this. It’s still a struggle, but it’s doable. Take your time, you're not going to get Worlds of Hurt - Expert at the same time. This trophy could take up to or over an hour to get.