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