Here is the full list of all 20 Super ComboMan: Smash Edition achievements.
1000 Smashes Given
100 Dodoco workers defeated
100 Hit Combo Achieved
50 Wall Smashed
50 Hit Combo during Boss P Battle
50 Hit Combo during Fapjack Battle
50 Hit Combo during the first Gorilla Grip Battle
Make it through a stage with full health bar
Buy all moves and perks
50 Crates Smashed
Collect all stickers in game
Complete 1st Stage
Complete the game
Consume one of each of the health pick up
Get highest rating on every stage
100 Back Smashes Delivered
Parry 50 Attacks
50 Fireballs hit enemies
100 Fire Uppercuts hit enemies
Purchased every perk in the combo store