Here is the full list of all 27 Scribblenauts: Showdown trophies - there are 8 bronze, 12 silver, 6 gold and 1 platinum.
Win a game of Get Served! without losing any health.
Create one of Maxwell's brothers in Sandbox Play or a Wordy game.
Unlock all 8 Sandbox levels.
Complete a 25 round Versus match.
Play every Speedy game at least once.
Complete a Showdown with 4 players.
Play every Wordy game at least once.
Shutout a player in Versus by winning every single round.
Play Sandbox with two players.
Win a game of Balancing Act! without dropping any of your objects.
Win a game of Super Sprint! without hitting an obstacle.
Win 5 consecutive games against a single player.
Earn 100 Starites.
Earn 25 Starites.
Create a custom Scribblenaut.
Unlock all other trophies.
Create all 15 custom Scribblenauts.
Create 100 Sandbox objects.
Complete a 9 round Versus match.
Complete a 15 round Versus match.
Score at least 1500 points in Drone Drop!
Create a chain of 10 objects in Rocket Rubble!
Knock down a tower in 8 launches in Tower Topple!
Make it to the finish line in Take Flight! with full health.
Unlock all the custom Scribblenaut parts.
Unlock all custom Sandbox objects.
Unlock all vehicles in the game.