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.
Unlock all trophies for Sly Cooper's first outing
Open all vaults
Learn Sir Augustine of Cooper's Briefly Defy Gravity Technique
Find all the blueprints
Collect a voodoo blueprint
Max out all shadow techniques
Upgrade your shadow
Max out all slow motion techniques
Upgrade your slow motion technique
Collect a blueprint from Muggshot
Defeat Clockwerk
Track down Clockwerk
Defeat Panda King
Collect some snowy blueprints
Learn Sir Andrew Cooper's Thief Replica Technique
Learn Suzanne Cooper's Water Safety Technique
Learn B.F. Cooper's Speed Up the Clock Technique
Collect some watery blueprints
Learn Rob McCooper's Explosive Hat Technique
Learn Karen Cooper's Coin Magnet Technique
Learn Slytunkhamen's secret move
Defeat Mz. Ruby
Find all the dive moves
Learn Dev Cooperinda’s Slow Motion Jump
Enter the Voodoo swamp
Defeat Muggshot
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!