Here is the full list of all 36 Sly Cooper and the Thievius Raccoonus trophies - there are 22 bronze, 8 silver, 5 gold and 1 platinum.
Defeat Clockwerk
Track down Clockwerk
Defeat Panda King
Learn Karen Cooper's Coin Magnet Technique
Learn Slytunkhamen's secret move
Defeat Mz. Ruby
Find all the dive moves
Enter the Voodoo swamp
Defeat Muggshot
Learn Dev Cooperinda’s Slow Motion Jump
Enter Muggshot's territory
Defeat Sir Raleigh the Frog
Learn Drake Cooper's Fast Attack Dive
Collect all clue bottles in any level
Collect 99 coins
Collect 60 coins
Start out on your Cooper adventure
Collect a police file from Carmelita
Collect a single coin
Enter the world of Sly Cooper!
Unlock all trophies for Sly Cooper's first outing
Collect some snowy blueprints
Collect some watery blueprints
Collect a blueprint from Muggshot
Learn Rob McCooper's Explosive Hat Technique
Upgrade your shadow
Upgrade your slow motion technique
Learn Sir Andrew Cooper's Thief Replica Technique
Learn Sir Augustine of Cooper's Briefly Defy Gravity Technique
Collect a voodoo blueprint
Learn B.F. Cooper's Speed Up the Clock Technique
Learn Suzanne Cooper's Water Safety Technique
Max out all slow motion techniques
Max out all shadow techniques
Find all the blueprints
Open all vaults