There are 51 Trophies that can be collected.

BRONZE

Rude Awakening
Re-Enter the Animus.

Mystery Guest
Complete Sequence 1 & 2.

How D'ya Like Them Apples
Complete Sequence 3.

Heroes are Born
Complete Sequence 4.

The Day the Templars Cried
Complete Sequence 5.

Caged Wolf
Complete Sequence 8.

Grim Expectations
Complete Sequence 10.

Difficult End
Complete Sequence 11.

An Extraordinary Man
Complete the Encyclopedia of the Common Man.

Patent Not Pending
Craft one of Franklin's inventions to decorate your Manor.

House Party
Recruit any of the Artisans and see them settled on the Homestead.

Original Gamer
Win a game of Fanorona, Morris and Bowls on the Homestead.

Bring Down the House
Explore Fort Wolcott.

Kidd Gloves
Uncover the mystery of Oak Island.

Entrepreneur, not Pirate!
Complete all 12 Privateer Contracts.

Tumblehome
Upgrade the Aquila.

By Invitation Only
Be invited to join a Club.

Monopoly Man
Send a convoy to Boston, New York and the Frontier.

Blowing in the Wind
Retrieve every page for one of Ben Franklin's Almanacs.

Multitasking
Complete 50% of the Progress Tracker entries.

Spit Roast
Perform a double assassination using a musket.

Circus Act
Kill 15 guards with a single cannon shot.

Predator
Hang 5 enemies by using rope darts.

Prince of Thieves
Loot a convoy without killing any of its guards.

Whit's fur ye'll no go by ye!
Block a firing line 5 times by using a human shield.

Jager Bomb
After becoming fully Notorious, kill 10 Jagers before losing your notoriety.

Magna cum Laude
Have a Trainee reach the Assassin Rank.

Coureur des Bois
Exchange undamaged pelts at all different general stores.

Eye Witness
Witness a predator killing an enemy.

Hunter/Killer
Reach sequence 10 in a map on Wolfpack multiplayer mode.

Winning Team
Be on the winning team at the end of a multiplayer game session.

Personalized
Customize your multiplayer Profile and Character.

SILVER

No Good Deed Goes Unpunished
Open the Temple Door and learn Desmond's fate.

Tea is for Englishmen
Complete Sequence 6.

The Whites of Their Eyes
Complete Sequence 7.

Two if by Sea
Complete Sequence 9.

Perfectionist
Complete 100% of all main mission constraints.

A Complete Set
See all the optional characters settled at the Homestead.

All Washed Up
Complete all Naval Missions aboard the Aquila.

In Good Standing
Complete all challenges for any of the Clubs.

Man of the People
Liberate all districts in Boston OR New York.

Completionist
Complete ALL progress tracker grid entries.

Fin
Complete each of the epilogue missions unlocked after the credits roll.

Abstergo Entertainment
Reach level 20 in the multiplayer mode.

The Truth Will Out
Unlock a hacked version of one of the Abstergo videos in the story quest.

GOLD

The Sum of Truth
Complete Sequence 12.

PLATINUM

Master Assassin
Get every trophy.

4 SECRET

http://www.ps3trophies.org/game/assassins-creed-iii/trophies/