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