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