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