Here is the full list of all 39 SUPER BOMBERMAN R 2 achievements.
Competed in a Graded Match with a castle you built
Castle uploaded
You won a battle with all 8 Brothers
You won a Standard Game
All Ellon types protected
Cleared Story Mode
Cleared Unknownstar
You won a Battle 64 with your life at 2
All Ellon types spotted
Cleared Aquastar
You came 1st in a Battle 64
Online Battles:First across the finish line (Attack Side)
Online Battles:You won by picking up a key dropped by another player (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)
100 Gimmicks destroyed
Online Battles:You won (Castle Side)
Online Battles:You used a weapon
Cleared Planet Fullvita
World Level maxed out
You maxed out all your stats
Online Battles:You died by your own bomb
You won a Grand Prix
You rode on a Louie
Base raid was successful
100 small fry enemies defeated
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 made a comeback on a Revenge Cart
You got pushed into the Abyss