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