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