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