Here is the full list of all 33 Polychromatic achievements.
Complete a game.
Earn an extra life while having no extra lives.
Die the first time.
Kill an enemy.
Kill 100,000 enemies.
Complete 100 games.
Get a score of 250,000 in Endless Mode.
Get a score of 850,000 in Endless mode.
Get a score of 2,000,000 in Endless mode.
Get a score of 5,000,000 in Endless mode.
Get a score of 250,000 in Timed mode.
Get a score of 550,000 in Timed mode.
Get a score of 850,000 in Timed mode.
Get a score of 50,000 in One-Life mode.
Get a score of 350,000 in One-Life mode.
Get a score of 850,000 in One-Life mode.
Earn 250,000 points without dying.
Earn 50,000,000 points across all games.
Reach wave five without firing the gun.
Reach wave 10 without dying.
Reach wave 20.
Reach wave 25.
Reach wave 30.
Have at least six extra lives, blasts, and dashes at one time.
Have nine extra lives at one time.
Have nine blasts at one time.
Have nine dashes at one time.
Kill 40 enemies with one blast.
Kill 10 enemies with one dash.
Fire off 100 blasts.
Dash 100 times.
Get shot five times.
Finish Timed Mode with no kills and no deaths.