Here is the full list of all 12 Super Bomberman R Online achievements. It takes around 1-2 hours to unlock all of the achievements on Windows.
Win a battle with all 8 Brothers
Come 1st in a Battle 64
Win a game while riding Louie
Win a Grand Prix
Get a PERFECT in a Grand Prix
Finish a round in a Grand Prix without dying
Died by destroying a Block
Died by your own bomb
Win a game without picking up a single item panel
Win a Standard Game
Get pushed into the Abyss
Dominate an area in a Battle 64