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