Here is the full list of all 13 Krinkle Krusher (HK/TW) trophies - there are 9 bronze, 3 silver and 1 gold.
Complete every stage with 3 stars and get all magical gems.
Complete every stage with "Flawless Victory".
Imprison the King Krinkle forever!
Upgrade the 5 elemental rings to level 5.
Defeat the Kranium Krinkle.
Defeat the Mecha Krinkle.
Knock back the King with spikes and tornados.
Feed Kranium with some spicy krinkles!
Knock back the Mecha Krinkle with his own bomb.
Get all spells.
Use an elemental krinkle explosion to kill 4 other krinkles.
Unlock the Mage's Room.
Show who's the best by defending the castle!