Here is the full list of all 32 Super Bomberman R achievements.
Beat Planet Lalaland on Story Mode
Beat Planet Brainwave on Story Mode
1000 Blocks Destroyed
Beat Planet Timbertree on Story Mode
Used 1000 Bombs
Beat Planet Technopolis on Story Mode
Maximized your blast radius
Maximized your movement speed
Carried the MAX number of Bombs
Got defeated by your own bomb.
Over 5 Bombs Exploded as a Combo
Used 1,000,000 Bombs
Over 10 Bombs Exploded as a Combo
1,000,000 Blocks Destroyed
Won without getting a panel
Lost to a Revenge Cart
Won with a Revenge Cart in a 4+ Player Multiplayer Battle
Tied with a Time Up
Played 100 Multiplayer Battles
Played 1,000 Multiplayer Battles
Won a 4 Player Multiplayer Battle
Won a 8 Player Multiplayer Battle
Created a Room and Battled
Created a Room and Battled 10 times
Created a Room and Battled 100 times
Beat Beginner on Story Mode
Beat Veteran on Story Mode
Beat Expert on Story Mode
Beat Planet Scrapheap on Story Mode
Beat Black Hole on Story Mode
Won a battle with each of the 8 Bomberman Brothers
Won a battle with each of the 5 Dastardly Bombers