Here is the full list of all 17 Pixel Star achievements.
Destroy Torktus SS
Destroy the Beholder
Destroy the Slurm
Destroy Static II
Chase a rainbow for awhile
Crash into a star
Have a ridiculous number of drones
Maximize lasers
Maintain Turbo for 15 seconds
Maximize shield defense
Die 100 times
Survive for 20 minutes
Obtain the maximum score multiplier
Reach 99,000 points in one run
Reach 1,000,000 points in one run
Defeat all bosses in one run
Defeat all bosses without taking damage