Here is the full list of all 32 Super Bomberman R achievements.
Over 5 Bombs Exploded as a Combo
Got defeated by your own bomb.
Used 1000 Bombs
Used 1,000,000 Bombs
Over 10 Bombs Exploded as a Combo
1000 Blocks Destroyed
1,000,000 Blocks Destroyed
Won without getting a panel
Maximized your blast radius
Carried the MAX number of Bombs
Maximized your movement speed
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 Technopolis 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