Here is the full list of all 36 Sly 3: Honor Among Thieves trophies - there are 22 bronze, 8 silver, 5 gold and 1 platinum.
Defeat Black Baron
Purchase Hover Pack
Defeat Muggshot
Ask Penelope for help
Defeat mask-powered Carmelita
Obtain the Paraglider
Finish the bar room brawl
Collect 1,000 coins
Dump off the truckload of scorpions
Collect 500 coins
Meet the Guru
Defeat Octavio
Destroy pumps
Use a Sly disguise in Venice
Complete the canal boat chase in Venice
Get close to Carmelita
Complete Prologue
Unlock all trophies for Sly Cooper's final outing. . . final? Really?
Slow down Dr. M as Bentley and Murray
Stop the vampires
Complete Dynamic Duo
Purchase the Alarm Clock
Collect Dimitri's diving gear
Carmelita to the rescue again
Purchase Shadow Power 2
Defeat Chinese Dragon
Defeat LeFwee
Defeat Crusher
Defeat Dr. M
Complete 75% of the game
Complete 50% of the game
Purchase Sly Spin Attack 3
Purchase Sly Jump Attack 3
Collect 2,500 coins
Purchase Diablo Fire Slam
Complete 100% of the game