Here is the full list of all 35 HyperNova achievements.
Defeat more than 1000 enemies
Defeat more than 3000 enemies
Defeat more than 10000 enemies
Clear the game
Clear the game with no continue
Clear overclock mode
Clear overclock mode with no continue
Total score over 400000
Total score over 500000
Total Score over 600000
Total score over 700000
Clear wave1 with no damage
Clear wave2 with no damage
Clear wave3 with no damage
Clear wave4 with no damage
Clear wave5 with no damage
Clear the game with no damage
Clear wave1 in overclock mode with no damage
Clear wave2 in overclock mode with no damage
Clear wave3 in overclock mode with no damage
Clear wave4 in overclock mode with no damage
Clear wave5 in overclock mode with no damage
Clear overclock mode with no damage
Defeat the DiskShip
Defeat the MotherComet
Defeat the MonsterFlower
Defeat the AcientGolem
Defeat the DualShip
Defeat the Destroyer
Defeat the DiskShip in overclock mode
Defeat the MotherComet in overclock mode
Defeat the MonsterFlower in overclock mode
Defeat the AcientGolem in overclock mode
Defeat the DualShip in overclock mode
Defeat the Destroyer in overclock mode