Here is the full list of all 12 DRAGON NINJA BYOKA achievements.
Kill 10 enemies
Kill 100 enemies
Kill 1000 enemies
Kill 10,000 enemies
Defeated Boss Wrender John
Defeated Boss Rakata the Daemon
Defeated Boss Chaos Helicopter
Defeated Boss Mutant X
Defeated Boss Gemstone Sentinel
Chose the Peace of the Past
Defeated Zangul the Chaos Serpent
Had a Change of Heart