Here is the full list of all 20 Super Crush KO achievements.
Complete the tutorial
Complete Little Shibuya
Complete Greenwood Park
Complete West West Pine West
Complete the game
Defeat Mecha One in 1m 30s or less
Defeat Mecha Two without taking damage
Defeat Mecha Three without jumping
Defeat Mecha Four without using Super Beam KO
Complete a level with an A Rank
Complete a level with an S Rank
Complete a level with an S+ Rank
S Rank every level in an area
Get a 20-hit combo
Get a 40-hit combo
Complete an arena stage with a Perfect Combo (excluding tutorial level)
Get 5 Perfect Combos over the entire game
Get 15 Perfect Combos over the entire game
Finish a level without taking damage (excluding tutorial level)
Dodge through 15 enemy bullets in a level