There are 45 Trophies that can be collected.

BRONZE

Diarist
Collect every diary page

Egg Hunter
Collect every alligator egg

Statuette Collector
Collect every Mayan statuette

Climber
Climb 8848 meters

Survivor
Survive 5 alligator encounters

Charming
Charm 50 NPC's

Disguised
Change your persona 50 times

Shipmaster
Buy the maximum number of ships

Swamp Queen
Tree Run for 10 branches without touching the ground

Tree ninja
Complete 15 Air Assassinations from trees

Notorious
Move through New Orleans for 10 minutes in the Assassin Persona

Deadly Haystack
Kill 50 enemies from haystacks using the Blowpipe

Umbrella
Kill 25 enemies with the Parasol Gun

My 1st Dressing Chamber
Buy your 1st Dressing Chamber

Buy All Dressing Chambers
Buy every Dressing Chamber

Hangman
Perform 10 predator moves using the Whip

Mushroom Queen
Collect all the mushrooms collectibles

RHP Master
Synchronize all viewpoints

Fighter
Participate in 100 fights in multiplayer

Power master
Complete 30 economic missions in multiplayer

SILVER

Complete 100% of all Mission Constraints
Achieve 100% Synchronization in all Sequences

Human Shields
Block 10 firing lines with a human shield

Persona Collector
Collect every persona-specific collectible

Machete
Kill 5 guards in 15 seconds using only the Sugarcane Machete (without using the Chain Kill)

What is she doing?
Kill 7 guards on rooftops in the Lady Persona

Thief
Pickpocket 5000 écu

Poison
Use berserk poison to force an enemy to kill 5 enemies

Business Woman
Complete every Business Rivals mission

Pirates
Complete every Pirates mission

Bayou Fever
Complete every Bayou Fever mission

Liberation
Complete every Free Slaves mission

Completionist
Reach the maximum player level in the multiplayer

PLATINUM

Platinum Trophy
Collect all other 44 Trophies for this Trophy

12 SECRET

http://www.ps3trophies.org/game/assassins-creed-3-liberation/trophies/