Here is the full list of all 28 Nickelodeon All-Star Brawl 2 achievements.
Defeat a level 9 NPC in a 1v1 battle
Defeat an opponent without losing a single stock in a local or online battle
Clear Arcade with 1 brawler
Level up a Campaign Perk to its max level
Unlock all Campaign Perks
Defeat Vlad Plasmius in the Campaign
Defeat Shredder in the Campaign
Defeat the Flying Dutchman in the Campaign
Complete a Pop the Slime Balloons minigame level
Complete your first Campaign run
Defeat King Jellyfish in the Campaign
Play at least once with all standard brawlers in a local or online battle
Compete in 10 local or online battles
Compete in your first local or online battle
Customize your profile badge for the first time
Clear Arcade with 5 brawlers
Clear Arcade with 15 brawlers
Clear Arcade with all (standard) Brawlers
Complete an Arcade run without losing a single stock
Complete an Arcade run on the highest difficulty
Compete in 50 local or online battles
Compete in 100 local or online battles
Defeat three level 9 NPCs in a team-battle
Complete the Campaign's story
Defeat Sartana in the Campaign
Defeat Clockwork in the Campaign
Complete a Campaign run in the highest difficulty
Complete the Pop the Slime Balloons minigame with all (standard) brawlers