Here is the full list of all 19 Super Comboman: Dont Mash Edition achievements.
50 Wall Smashed
100 Dodoco workers defeated
50 Crates Smashed
Parry 50 Attacks
Make it through a stage with full health bar
Complete 1st Stage
1000 Smashes Given
100 Hit Combo Achieved
50 Hit Combo during Boss P Battle
50 Hit Combo during Fapjack Battle
50 Hit Combo during the first Gorilla Grip Battle
Buy all moves and perks
Complete the game
Consume one of each of the health pick up
Get highest rating on every stage
100 Back Smashes Delivered
50 Fireballs hit enemies
100 Fire Uppercuts hit enemies
Purchased every perk in the combo store