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