Here is the full list of all 13 Fat Princess: Piece of Cake trophies - there are 10 bronze, 2 silver and 1 gold.
Launch 25 princess attacks
Complete 250 cascades
8 match cascade
Complete 1 normal level
Complete 55 normal levels
Complete 10 challenge levels
Defeat 500 enemies
Purchase 12 hero upgrades
Die 300 times
Revive 50 heroes
Match 5000 diamonds
Achieve 555 match 5's
Use 6 power ups