Here is the full list of all 32 Spectrum achievements.
Exit the tutorial.
Complete one level.
Kick the bucket.
Unlock control over red.
Unlock control over yellow.
Unlock control over green.
Unlock control over blue.
Unlock control over purple.
Beat the game.
Unlock the Cool Cap.
Unlock the Rainbow Crown.
Unlock the Paint Bucket.
Collect a crayon.
Collect 10 crayons.
Collect 20 crayons.
Collect all crayons.
Jump 100 times.
Jump 500 times.
Jump 1000 times.
Collect 100 hue.
Collect 1000 hue.
Collect 5000 hue.
Ride the pale horse 100 times.
Bite the dust 1000 times.
Die shortly after respawning.
Beat the game without dying.
Collect all hats.
Complete all A and B sectors.
Go backstage.
Complete a level with very little time remaining.
Collect all hue in S2A2 without dying.
Complete every main level in the game.