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