Here is the full list of all 30 Killer Instinct Classic achievements worth 1,000 gamerscore.
Perform an ultra
Perform a humiliation
Spend 400 credits
Win 40 Matches with Chief Thunder.
Win 40 Matches with Cinder.
Win 40 Matches with Fulgore.
Win 40 Matches with Glacius.
Win 40 Matches with Jago.
Win 40 Matches with Orchid.
Win 40 Matches with Riptor.
Win 40 Matches with Sabrewulf.
Win 40 Matches with Spinal.
Win 40 Matches with TJ Combo.
Get a Perfect in Arcade with Spinal, Riptor and Sabrewulf
Defeat Eyedol with Chief Thunder
Defeat Eyedol with Cinder
Defeat Eyedol with Fulgore
Defeat Eyedol with Glacius
Defeat Eyedol with Jago
Defeat Eyedol with Orchid
Defeat Eyedol with Riptor
Defeat Eyedol with Sabrewulf
Defeat Eyedol with Spinal
Defeat Eyedol with TJ Combo
Defeat Eyedol with all characters
Defeat Eyedol using only one credit
Humiliate every character in the game
Perform an ultra with every character in the game
See all Victory Animations and Endings
Win a match in every arena