Here is the full list of all 39 SUPER BOMBERMAN R 2 achievements.
Complete all the achievements
You got pushed into the Abyss
Cleared Story Mode
World Level maxed out
Cleared Unknownstar
All Ellon types protected
All Ellon types spotted
Cleared Aquastar
Online Battles:You defeated 100 opponents using a weapon (Attack Side)
100 Gimmicks destroyed
You won a battle with all 8 Brothers
Online Battles:You won by opening the final treasure chest (Attack Side)
1000 parts placed
You made a comeback on a Revenge Cart
You maxed out all your stats
Online Battles:You won by picking up a key dropped by another player (Attack Side)
Online Battles:First across the finish line (Attack Side)
Online Battles:You won (Attack Side)
Online Battles:You won (Castle Side) not letting a single player on the Attack Side get a goal
Online Battles:You won without using weapons (Castle Side)
Competed in a Graded Match with a castle you built
Online Battles:You used a weapon
Online Battles:You won (Castle Side)
10 castles built
You came 1st in a Battle 64
You won a Battle 64 with your life at 2
You won a Grand Prix
Cleared Planet Fullvita
100 small fry enemies defeated
You rode on a Louie
Online Battles:You died by your own bomb
You won a Standard Game
Castle uploaded
Base raid was successful
Cleared a Secret Puzzle
Opened an Ellon Shutter
Castle built
HQ successfully defended
Spotted an Ellon