There are 12 Trophies that can be collected.

BRONZE

First Twist
Rotate a room for the first time.

Novice strategist
Win mission 9 against the computer.

Scout
Reveal 3 rooms in a row with 3 action points.

Executor
Eliminate 2 enemies with only one action point.

He had a thick skin!
Eliminate your opponent's Troll.

Flee!
Make at least 5 characters get out during the same game.

Pillage!
Leave with 2 Treasures during the same turn.

Sniper
Throw a Fireball at a distance of more than 8 squares from your target.

SILVER

Get ready for PlayStation®Network!
Finish the Training mode.

Don't forget to eat…
Finish at least 30 multiplayer games on PlayStation®Network.

Total respect
Collect more than 5000 points in Challenge mode.

GOLD

You are the new Arch-Mage!
Win a difficulty 12 game in Challenge mode.

http://www.ps3trophies.org/game/dungeon-twister/trophies/