Here is the full list of all 21 Super Comboman: Smash Edition trophies - there are 6 bronze, 6 silver, 8 gold and 1 platinum.
You collected all the cute little trophies
Make it through a stage with full health bar
1000 Smashes Given
50 Wall Smashed
Parry 50 Attacks
50 Crates Smashed
Complete 1st Stage
50 Fireballs hit enemies
100 Fire Uppercuts hit enemies
100 Dodoco workers defeated
100 Back Smashes Delivered
Purchased every perk in the combo store
Consume one of each of the health pick up
50 Hit Combo during the first Gorilla Grip Battle
50 Hit Combo during Boss P Battle
50 Hit Combo during Fapjack Battle
100 Hit Combo Achieved
Buy all moves and perks
Collect all stickers in game
Get highest rating on every stage
Complete the game