This trophy is story-related and cannot be missed.
You will get this after progressing a bit into the game. Meeting up with your squad for the first time after landing, a cutscene will play and that is when you'll get this trophy (late in Chapter 1).

This trophy is story-related and cannot be missed.
When you infiltrate your first real Korean building to rescue hostages in Chapter 2.

This trophy is story-related and cannot be missed.
When you get into the argument with Prophet over the real reason you are on this island your character will say the name of this trophy and that is when it should pop. Near the end of Chapter 2.

This trophy is story-related and cannot be missed.
When you reach and enter the dome facility and see the cutscene with General Kyong this trophy will pop shortly after. It is obtained midway through Chapter 3.

This trophy is story-related and cannot be missed.
You will get this at the end of Chapter 3 after defeating the enemy Korean nanosuits.

This trophy is story-related and cannot be missed.
You'll get this trophy early in Chapter 4. The first task you are given at the beginning of the chapter is to take out 2 AA guns and then after you do that there is 1 more that shows up that you need to destroy. After you take out all 3 the trophy is yours.

This trophy is story-related and cannot be missed.
You get this trophy after you laze the aircraft carrier for a tactical strike near the end of Chapter 4.

This trophy is missable (but can be gotten via chapter select on Onslaught which is Chapter 5). When you get to the area where you can clear out Boxcars on train tracks for the secondary objective make sure you kill everything around the area including above you on the ridge. Wait there until the trophy pops before moving on.

This trophy is story-related and cannot be missed.
You get this at the end of Chapter 5 after you meet up with your team to proceed forward.

This trophy is missable (but can be gotten via chapter select on Onslaught, which is Chapter 5). You start the chapter with a tank, if you get out of the tank and proceed to enter another vehicle or just progress on foot to the objective without the original tank you were in you will not get this trophy. Do not worry if your tank is severely damaged and you die, you'll just restart @ your latest checkpoint with the same tank at half health. If you are really having trouble with this play the chapter Onslaught on easy.

This trophy is story-related and cannot be missed.
You get this partway through Chapter 6 after progressing into the mines.

This trophy is story-related and cannot be missed.
Obtained in Chapter 6, this serves as a mini boss battle and is fairly easy even on Delta. Just run around in stealth looking for SMG ammo and wait for Kyong to keep reappearing then exit stealth mode when you've flanked him and shoot his head with your SMG. Repeat 4-5 times until he is dead.

This trophy is story-related and cannot be missed.
In Chapter 7 you'll be stuck underground making your way through the Alien facility, you will get this at the end of the area (midway through the chapter) where you escape through a bright light.

This trophy is story-related and cannot be missed.
You will meet up with Prophet in Chapter 7 shortly after exiting the Alien underground base and progressing a bit. You simply have to fight your way through the Aliens until the end of the chapter. Don't worry about Prophets suit level as shown on your screen. As long as he is not getting hit by enemies it will recover.

This trophy is story-related and cannot be missed.
You'll get this at the end of Chapter 8 after you've fended off the many giant squid-like Aliens with AA guns. One of the COs will say this line as you board the VTOL and that is when the trophy pops.

This trophy is story-related and cannot be missed.
You will have to go back to the flight deck after picking up the TAC Cannon to defeat the giant spider-like Alien that killed Strickland as you left in the VTOL from the previous chapter. Simply unload 4-5 Minigun clips into it and it'll go down and you'll get this trophy.

This trophy is story-related and cannot be missed.
You'll get at the end of Chapter 10 after defeating the Alien mothership. What you want to do first is take out the turrets (2 on each side) from cover with a Gauss Rifle (4 shots to each turret destroys them) and then wait for your team in the VTOL to get in close to disable the right side of the ship (in the meantime you fight giant Alien squids which come from the ship). When the right side is disabled (Your team will notify you) switch to the TAC Cannon, lock on (without getting killed) and fire to destroy that side. Same procedure for the left side and the center when it opens up. Be aware of the ships one-shot kill giant blue beam. Always move from cover to cover around the flight deck.

See the Cool In A Crysis trophy.

See the Cool In A Crysis trophy.

See the Cool In A Crysis trophy.

This trophy is story-related and cannot be missed.
Beat the game. This trophy will pop during the credits. I made sure to wait until it popped before exiting out of the credits screen.

Delta mode is super easy compared to other FPSes. If you can get through any Call of Duty game on Hardened then this will be a cakewalk. You can and it is recommended that you approach enemies from a distance with stealth so you have a surprise advantage. The key to winning is not getting swarmed in a place without cover. Use weapon attachments (via holding Select), stealth and cover and this trophy will pose no problem at all. I obtained this trophy from playing new game all the way through the campaign on Delta but it will also unlock via chapter select if you choose to play the game on an easier setting first. This trophy will pop during the credits. I made sure to wait until it popped before exiting out of the credits screen.

See the Perfect Soldier trophy.

See the Perfect Soldier trophy.

Secondary objectives are the yellow objective markers on your radar (located in the bottom right hand of your screen). If you want a detailed view of the secondary objective as well as it's exact location on the map of the area you are in press the SELECT button. All secondary objectives are fairly easy and involve something like getting to an enemy bunker to upload intel via an interactive computer. If you are having trouble replay the chapter with the secondary objective on easy. This trophy will pop on the Awakening level if you completed all previous secondary objectives prior.

You will see enemy helicopters by North Korean soldiers throughout various chapters later on in the game (starting on chapter 3). Simply take them out with the missle launcher weapon (it requires 2 direct hits from it). You can easily farm the Onslaught level as it is super easy to take out a helicopter from your tank. Simply shoot it down hit start and restart from checkpoint.

Like the helicopter trophy simply use rocket launchers to destroy enemy tanks. You likely won't need to farm this at all so don't bother because when you get to the Onslaught level there are over 10+ tanks scattered around as you progress through the level which are easy targets for you to take out.

Customize your weapon by holding down the SELECT button and equip weapon mods via triangle, circle, square, X and R1. The first time you'll be able to get this trophy is on chapter 4 because you are unable to equip specialty ammo until you are that far in the game. You can find incendiary rounds when you're going around taking out the AA guns, the other attachments are basically a given as you start with a default on every other slot.
I got this trophy with the FY71 with this configuration:
Incendiary Ammo (Magazine), Silencer (Barrel), Tactical Light (Side Rail), Grenade Launcher (Under-Barrel), Reflex Sight (Rail)

You'll get this without even trying most likely even when playing on any difficulty. It is essentially unmissable.

You can go back and farm a specific chapter for enemy kill on easy. Any chapter will do, The tank level Onslaught is a quick way to easily rack up kills and so is chapter 5.

Easiest done if you snipe an enemy although you can take out a tank/helicopter with a rocket launcher at a far distance. I did this on Chapter 4: when you are suppose to take out the AA guns, if you have the sniper with the sniper scope from the previous ending of the last chapter (where you fight the Korean nanosuits for the first time) snipe from the ledge before you drop down into the water to get to the AA guns to score this trophy easily. I sniped someone on the boat patrolling the waters. The sniper scope does show the distance you are zoomed in on when you ADS.

Every time you get a new weapon in a chapter make it a priority to kill an enemy with it. When you kill enemies look for the weapon they drop as well as it may be unique. You will not get this trophy until very late in the game because the last weapon (Alien one) is not available until one of the final chapters. You may only need to kill enemies with guns and not explosives, I killed enemies with everything though.
Full Weapons List:
Pistol (Starting Weapon)
Scar (Starting weapon)
FY71 (Default enemy weapon)
SMG (Enemy weapon, found in chapter 4+)
Precision Rifle (Sniper, picked up in various levels)
Shotgun (Common enemy weapon)
Grenade (Found in various chapters)
C4 (Found in chapters where you have to take out objectives like tanks, AA guns, etc)
Missle Launcher (Found in various chapters where you have to take out objectives)
Guass Sniper (Given to you as a pick up at the end of Onslaught, get from VTOL)
Minigun (Picked up in later chapters, some enemy nanosuits carry it, for example in Chapter 5)
Alien MOAD (Prophet will drop the weapon shortly after you meet him, pick it up)

All you have to do for the trophy is equip one of every weapon attachment which you will get if you are actively switching weapons and picking up weapons from fallen enemies (for the Weapons Master trophy).
Full Weapon Modification List:
Silencer (Triangle) - Default on SCAR
Flashlight (Square) - Default on SCAR
Laser Pointer (Square) - Default on Pistol
Tactical Attachment (Circle) - Default on SCAR
Grenade Launcher Attachment (Circle) - Default on SCAR on Chapter 6
Iron Sights (X) - Default on SCAR
Reflex Sight (X) - Default on SCAR
Assault Scope (X) - Picked up randomly throughout all chapters on FY71
Sniper Scope (X) - Chapter 3 @ the end, kill Korean Nanosuits one will drop a sniper with this attachment
Incendiary Ammo (R1) - Picked up in Chapter 4+, scattered around enemy ammo caches
Explosive Ammo (R1) - Picked up in Chapter 4+, scattered around enemy ammo caches

Simply run up to enemy and press and hold square and Nomad will pick up the poor sucker and choke him out. Then press square again to throw the enemy. This is actually an efficient way to kill enemies because it's automatic KO. Do this 20 times and the trophy is yours, the count is also cumulative and can be done over the course of the campaign or chapter select.

You'll likely get this naturally as you sprint to objectives. Simply run around with L3 to sprint (You do not need energy to super sprint, can be normal sprinting). The count is cumulative and can be done over the course of the campaign or chapter select.

You can get this in the first chapter when you reach the Korean base of operations. There will be reinforcements called in and you can maintain stealth and individually take out each one without being spotted from a distance. If you are spotted you can restart checkpoint. There are also various other locations you can get this trophy later in the game as well, if you see a large group of enemies throw a nade from cover and if it kills all of them you will also get this trophy.

The first time (and the best time) to get this trophy is the first time you are introduced to the enemy Korean Nanosuit at the end of Chapter 3. You will need to kill 3-4 of them in order to get an extraction from the area. They can go invisible but it is still easy to see them. Enter armor mode and hold triangle to equip your fists. Run up to the enemy and press R1 or R3 to punch with either hand. Just keep pressing either button until the enemy is on the ground dead and you'll receive this trophy shortly after.

You can get this trophy throughout the game but the easiest spot is in Chapter 1 when you touch the first piece of land after dropping from the plane there will be a turtle in front of you simply pick it up and you'll get this trophy. Wait for the trophy to unlock and then put it down.

Simply press up on the d-pad to bring up your visor. You can zoom in with L1 and tag enemies by just getting the visor reticule on the enemy (and it will auto tag them on your radar). Do this 30 times across the course of the campaign or chapter select. The count is cumulative.

Pick up random objects in the world with square and throw them at weaken enemies. Recommended to do this trophy on easy and can be done on any chapter. You can soften the enemy up with bullets to lower there health so it takes less throws of the object to kill them.