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