Here is the full list of all 38 Kyurinaga's Revenge trophies - there are 24 bronze, 8 silver, 5 gold and 1 platinum.
Finish level 7 without losing a life
Collect 75% of scrolls
Finish all levels in co-op mode
Finish the game in normal mode
Finish the game in hard mode
Finish the game in easy mode
Complete level 10
Finish a level without losing a life
Kill a Pea using his own kama
Complete level 9
Defeat Voldemaru and Kyurinaga
Collect 50% of scrolls
Complete level 8
Use a kunai to kill a Parachute Chili
Kill 5 Patrol Chilis using Broccoli's kunais
Kill 10 peas
Defeat Ka, Zo and Ku brothers
Defeat Itoshi
Finish a level without activating any checkpoint
Complete level 7
Complete level 6
Complete level 5
Defeat 200 enemies in Horde Mode
Don't miss a combo during an entire combat (not applicable to Horde Mode)
Defeat Muteki
Collect 25% of scrolls
Complete level 4
Complete level 3
Complete level 2
Complete level 1
Collect all trophies
Finish the game in Inferno mode
Collect all golden coins
Collect 100% of scrolls
Kill 5 Patrol Chilis using Kaoru's explosive traps
Finish all levels in 1 player mode
Push your partner to a certain death (Kyurinaga's Castle Mode)
Defeat 850 enemies in Horde Mode