Here is the full list of all 37 Kyurinaga's Revenge achievements.
Finish level 7 without losing a life
Push your partner to a certain death (Kyurinaga's Castle Mode)
Defeat 200 enemies in Horde Mode
Finish the game in easy mode
Finish the game in normal mode
Finish the game in hard mode
Collect all golden coins
Collect 100% of scrolls
Finish all levels in 1 player mode
Complete level 10
Complete level 9
Defeat Voldemaru and Kyurinaga
Complete level 8
Collect 75% of scrolls
Use a kunai to kill a Parachute Chili
Kill 5 Patrol Chilis using Kaoru's explosive traps
Kill 5 Patrol Chilis using Broccoli's kunais
Defeat Ka, Zo and Ku brothers
Defeat Itoshi
Complete level 7
Complete level 6
Complete level 5
Collect 50% of scrolls
Defeat Muteki
Complete level 4
Kill 10 peas
Collect 25% of scrolls
Complete level 3
Finish a level without activating any checkpoint
Complete level 2
Finish a level without losing a life
Kill a Pea using his own kama
Don't miss a combo during an entire combat (not applicable to Horde Mode)
Complete level 1
Finish the game in Inferno mode
Finish all levels in co-op mode
Defeat 850 enemies in Horde Mode