Here is the full list of all 45 Assassin's Creed III Liberation trophies - there are 22 bronze, 21 silver, 1 gold and 1 platinum.
Kill an enemy from a tree, with the blowpipe, while using eagle vision
Survive 5 alligator encounters
Complete Sequence 4
Complete Sequence 3
Kill 5 guards in 15 seconds using only the Sugarcane Machete (without using the Chain Kill)
Move through New Orleans for 10 minutes in the Assassin Persona
Complete Sequence 2
Tree Run for 10 branches without touching the ground
Complete Sequence 1
Buy your 1st Dressing Chamber
Collect all other 44 Trophies for this Trophy
Complete Sequence 5
Complete Sequence 6
Complete Sequence 7
Complete Sequence 8
Complete the game (fake ending)
Kill all Citizen E and experience the true ending
Achieve 100% Synchronization in all Sequences
Block 10 firing lines with a human shield
Collect every diary page
Collect every alligator egg
Collect every Mayan statuette
Collect every persona-specific collectible
Climb 8848 meters
Charm 50 NPC's
Change your persona 50 times
Buy the maximum number of ships (8)
Complete 15 Air Assassinations from trees
Kill 7 guards on rooftops in the Lady Persona
Kill 50 enemies from haystacks using the Blowpipe
Kill 25 enemies with the Parasol Gun
Buy every Dressing Chamber
Pickpocket 5000 écu
Perform 10 predator moves using the Whip
Collect all the mushrooms collectibles
Use berserk poison to force an enemy to kill 5 enemies
Hang an enemy on the gibbet at the Place d'Armes
Synchronize all viewpoints
Complete every Business Rivals mission
Complete every Pirates mission
Complete every Bayou Fever mission
Complete every Free Slaves mission
Participate in 100 fights in multiplayer
Complete 30 economic missions in multiplayer
Reach the maximum player level in the multiplayer