Here is the full list of all 23 Kromaia achievements.
Beat a boss without taking any damage.
Defeat Orion.
Unlock the Psi Armor.
Score 25,000 In Score Attack Mode.
Defeat Argos.
Unlock the Mu Armor.
Obtain the Spinner.
Defeat Teuthus.
Unlock the Tau Armor.
Defeat Vermis.
Unlock the Alpha Armor.
Unlock the Omega Armor.
Clear every dimension.
Complete the game.
Obtain every treasure.
Score 50,000 In Score Attack Mode.
Score 100,000 In Score Attack Mode.
Reach the Sun.
Reach the end and unlock Super-Frame Mode 1.
Reach the end for a second time and unlock Super-Frame Mode 2.
Unlock Super-Frame Mode 3.
Unlock Super-Frame Mode 4.
Achieve a x100 hit combo.