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