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