Here is the full list of all 24 Polyfury achievements.
Defeated the Spiteful Square!
Defeated the Pitiless Pentagon!
Defeated the Hyper Hexagon!
Defeated the Triangle Twins!
Defeated the Hateful Heptagram!
Defeated the Terrifying Tetrapod!
Defeated the Octagon Overlord!
Got a 3 star score on the Spiteful Square
Got a 3 star score on the Pitiless Pentagon
Got a 3 star score on the Hyper Hexagon
Got a 3 star score on the Triangle Twins
Got a 3 star score on the Hateful Heptagram
Got a 3 star score on the Terrifying Tetrapod
Got a 3 star score on the Octagon Overlord
Entered a cheat code
Defeated the Super Square without being hit
Defeated the Pitiless Pentagon with your laser
Defeated both of the Hyper Hexagon's mini triangles
Simultaneously defeated both of the Triangle Twins
Didn't get hit during the Hateful Heptagram's survival phase
Interrupted the Terrifying Tetrapod's teleport
Removed all the Octagon Overlord's shielding
Beat the gauntlet
Beat the gauntlet with a three star score.