Here is the full list of all 17 Pixel Star achievements.
Destroy Static II
Chase a rainbow for awhile
Destroy the Beholder
Have a ridiculous number of drones
Destroy the Slurm
Destroy Torktus SS
Crash into a star
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