Here is the full list of all 39 Toy Story 3 trophies - there are 22 bronze, 13 silver, 3 gold and 1 platinum.
Congratulations—you’ve earned all the trophies for Toy Story 3!
Reach Zurg’s base without losing all your health
Finished the Prison Break without ever tripping an alarm
Achieve gold on all carnival games
Explored all the objects on the map
Purchase every item in the Toy Store
Collect all the Gold Stars
Finished "Muffin to Fear"
Gather every collectible in the game
Find all the Regular Cards
Find all the hidden aliens
Find all the Special Cards
Finished "Trash Thrash"
Collect all of Andy's Memorabilia
Finished "Hide-N-Sneak"
Finished "Witch Way Out"
Find all the hidden townspeople
Finished "Fair Play"
Collect all of Zurg's Parts
Finished "To Infinity and Beyond"
Finished "Hold the Phone"
Complete all Pict-O-Matic missions
Complete 1 disc of Pict-O-Matic missions
Complete all Toy Camera missions
Find all 6 discs of Pict-O-Matic missions
Hit 15 Paratrooper targets
Earn a bronze medal in a vehicle challenge
Purchase Zurg's Spaceport
Purchase Sid's Haunted House
Purchase Lotso's Enchanted Glen
Defeat Mayor Hamm in the Woody's Roundup boss battle
Save Mayor Hamm from the bandits
Blow up the dam and expand your town
Earn a gold medal in a vehicle challenge
Earn a silver medal in a vehicle challenge
Buy a toy from the Toy Store
Finish the Woody's Roundup tutorials
Finished "Loco Motives"
Rescue all the orphans on the Train