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