Here is the full list of all 15 Crimson Trigger achievements.
Reach Level 15
Complete the Intro Stage
Complete any stage without using any skill
Complete any stage without taking damage
Complete the game once
Complete the game in hard mode
Complete the game in insane mode
Defeat Chutcha
Defeat Chutcha in insane mode
Collect all abilities
Complete any stage without using normal attack
Collect 9 lives
Reach Level 30
Complete Final stage without using any skill
Collect all Crimson Tank