Here is the full list of all 30 Killer Instinct Classic achievements worth 1,000 gamerscore.
You won 40 Matches with Chief Thunder.
You won 40 Matches with TJ Combo.
You won 40 Matches with Saberwulf.
You saw all victory animations and endings
You defeated Eyedol with Sabrewulf
You defeated Eyedol with all characters
You won 40 Matches with Jago.
You won 40 Matches with Riptor.
You won 40 Matches with Spinal.
You won 40 Matches with Glacius.
You won a match in every arena
You defeated Eyedol with Spinal
You defeated Eyedol with Orchid
You spent 400 credits!
You defeated Eyedol with Jago
You performed an ultra with every character in the game
You defeated Eyedol with Chief Thunder
You defeated Eyedol with Glacius
You humiliated every character in the game
You won 40 Matches with Fulgore.
You defeated Eyedol with Riptor
You got a Perfect in Arcade with Spinal, Riptor and Sabrewulf
You performed an Ultra!
You defeated Eyedol with Fulgore
You defeated Eyedol with TJ Combo
You defeated Eyedol using only one credit
You won 40 Matches with Orchid.
You performed a humiliation!
You defeated Eyedol with Cinder
You won 40 Matches with Cinder.