Complete any 10 of the execution styles in the game. This trophy has to be completed before you eliminate the last family or else you can’t unlock it and you will have to start a new game. These HAVE to be done on mobsters. Doing them on civilians, members of your own family, and police will not count. Phamtruax wrote a good guide for the execution styles and described them better than I could. Here's the link for that: Execution Styles Guide - PS3Trophies.org

To do this, first you have to do a favor for someone. The people that you have to do the favor for have key icons above their heads. The favors range from burglaries (cracking a safe), sabotage (bashing up a shop), murder, bombing a business, and beating someone up. Once you complete the favor, the kill condition and location of the other family’s made man will appear in their family tree. An example of a kill condition is pushing him off of a building. You have to complete the kill condition or else that family member will not die.

A can’t miss trophy. Taking control of your third of the nine crime rings gives you this. When you reach the end of the game, you’ll have all the crime rings under your control. See Organized Crime for more details.

Another can’t miss trophy. Taking control of you fifth of the nine crime rings gives you this. When you reach the end of the game, you’ll have all the crime rings under your control. See Organized Crime for more details.

Break into any of the safes in the game. Every business has a safe somewhere inside (a couple have two in them). All four of the banks, the Federal Building in New York also have safes, the airport in Florida, and each family’s compound also have safes. You have to bring a made man with the Safecracking skill with you to be able to break into them. These you can go back after completing the game and break into. You’ll have all the businesses by then and won’t have to worry another family shooting at you.

You can’t miss this trophy. You get this at the beginning of the game when you create your character.

Upgrade the cheapest ability (Ready Weapon) of your first soldier for $500.

Pushing Start brings up the Don's View. Move over to a business owned by another family. You'll have the option to "Bomb" or "Send Men to Attack." Select "Bomb" by pushing square and send a member of your family with the Demolitions specialty.

Pushing Start brings up the Don's View. Move over to a business owned by another family. You'll have the option to "Bomb" or "Send Men to Attack." Select "Send Men to Attack" and you'll select which soldiers to send. Any member of your family can be sent.

The Level 2 guns are scattered throughout each of the three cities. There are five types of guns (pistols, magnums, shotguns, machine guns, and sniper rifles) and there is only Level 2 upgrade for each type and it is always in the same location. See Welcome to the Gun Show for more details.

The Level 3 guns are scattered throughout each of the three cities. There are five types of guns (pistols, magnums, shotguns, machine guns, and sniper rifles) and there is only Level 3 upgrade for each type and it is always in the same location. See Welcome to the Gun Show for more details.

There are four banks in the game, one in New York, two in Florida, and one in Cuba. Make sure that you have a made man with the Safecracker skill with you or will not be able to break open the safe or get into the vault. The easy way in is to bring a made man with the Demolition skill with you. On one of the sides of the bank, there will be a well with a dynamite icon next to it. You can set a bomb there and blow a hole in the building, right into the vault. Once you’re in, take the money, crack the safe, and get back to the safehouse as fast as you can.

Kill 100 mobsters by any means you want to use.

Kill 250 mobsters any way you would like.

Kill 25 mobsters any way you see fit. Shoot them. Run them over with a car. Push them off a building. Throw some dynamite at them. Or you can you can use your fists for the first 25 and get the “Blackhand Brutality” trophy at the same time.

Kill 25 mobsters using only your fists. Use L1 (left punch) and R1 (right punch) to beat down 25 mobsters and the trophy is yours (using L1 & R1 at the same time grabs them, by the way).

Kill 500 mobsters however you want.

Kill 150 mobsters using either a pistol, a magnum, a shotgun, a machine gun, or a sniper rifle.

Assign the maximum number of guards to a business that you take over. You can do this with the first business that you take over, even though you don’t have much money. Just set the number of guards to the maximum and edit out of the Don’s View. You can then go back in and edit the number of guards back down to save some money.

Another can’t miss trophy. After you have your third soldier, you’ll be told in a conversation to promote one of them to Capo.

Another can’t miss trophy. After you name your second Capo, you’ll be told in a conversation to promote one of them to Underboss.

Another can’t miss trophy. This will also come towards the beginning of the game when you’re told to expand your family.

Another can’t miss trophy. All the businesses that aren’t in a crime ring are businesses that you can take over to launder money. There are a handful in each city and nine total. They'll be marked by a cash register icon over them in the Don's View. By the time you complete the game, you’ll have control over all the extortable businesses.

This one you should get when bomb the complex of the first family you go up against. To unlock the compound, you have to take control of all the businesses owned by that family. Once you get into the family’s compound, follow the green X to the weak spot of the building. Have a soldier with the Demolitions skill set the bomb. You’ll be given about 20-30 seconds to get out of the building before the bomb goes off, so run like hell.

There are four banks in the game. Rob each one once and you’ll get this. Use the method outlined in Bank Job and you should have no trouble with this.

Kill 750 mobsters with any kind weapon. You’ll get to 750 mobster kills long before you finish the story.

You’ll get this one right after Second In Command. After promoting one of your men to Underboss, you can promote one of your soldier’s to Capo, and then recruit a new soldier to fill out the family tree.

Another can’t miss trophy. There are nine crime rings in total. When you reach the end of the game, you’ll have all the crime rings under your control. See Organized Crime for more details.

In each of the three cities, there are corrupt officials that you can do favors for. Doing these favors will return you a favor that you can use anytime you want. The favors you have to do are the same as the kill condition ones (busting up a store, beating someone up, breaking into a safe, bomb a business, or murder). The favors that you get are get your men out of the hospital quicker, rebuild a bombed business quicker, call in a raid on another family, call off a police pursuit, free men from jail, and in one unique case, lower a bridge. There are 12 corrupt officials in all, three in New York, six in Florida, and three in Cuba.

Here are the locations of each of the guns (thanks to Neeker at Gamefaqs for this):

Pistols
Level 2 - Silenced Pistol: Florida, found during a mission when you need to rescue one of Roth's soldiers.
Level 3 - Delta M1911: Florida, Mangano's Compound on the second floor.

Magnums
Level 2 - .44 Magnum Force: New York, Carmine Rosato's Compound on the second floor.
Level 3 - .501 Magnum Enforcer: Cuba, outside of the lighthouse that is next to the Battaglia Quarry Chop Shop.

Shotguns
Level 2 - Sawed-off: New York, Corleone's Compound, left of the main gate behind some bushes. Burn the bushes with an Arsonist.
Level 3 - Schofield Semi-Auto: Florida, Global Storage Chop Shop.

Machine Guns
Level 2 - MP38: Florida, Granados Compound, second floor.
Level 3 - Modified AK-47: Cuba, Battaglia Masonry, take the ladder in the office (on the left side, behind the desk, from where you enter the room) and go down into the tunnel. You’ll find it at the end of the tunnel.

Sniper Rifles
Level 2- Spitzer Centerfire : Florida, Emilio's packing company on the roof near the head of the racket. You’ll need an engineer to cut the fence.
Level 3 - Vintovka SR-98: Cuba, Almeida Compound on the second floor.

This trophy has to be completed before you eliminate the last family or else you can’t unlock it and you will have to start a new game. You have to do these on mobsters. They won’t count as completed if you do them on members of your own family, civilians, and police officers. Again, Phamtruax wrote a very good guide for these, and the link is provided again: Execution Styles Guide - PS3Trophies.org

Another can’t miss trophy. Certain businesses are linked together to form a crime ring. When you take over a business, you control a piece of the crime ring, but in order to get the bonus ability, you have to control all of the linked businesses. There are between two and four businesses per crime ring. Some of the crime rings are spread over two cities. The crime rings are drugs, gun running, adult entertainment, gambling, diamond smuggling, chop shops, prostitution, construction, and arms smuggling. Each crime ring has a different icon each business in the ring in the Don's View. There are nine total. When you own these, you get a bonus like bulletproof vests, extra ammo, or cheaper guards. Taking control of all the crime rings over all three cities earns you this. There are nine crime rings in total. When you reach the end of the game, you’ll have all the crime rings under your control.

Each business (plus the New York Federal building, each bank, and the Florida airport) and compound (except for the Corleone compound) has a safe somewhere inside. You’ll need to have a Safecracker with you to be able to break into them. You can do these after the story is completed, and you won’t have any interference from the other families while you’re trying to break into them.

Unlock all other 41 trophies to get this.