Here is the full list of all 23 Kromaia achievements.
Unlock the Alpha Armor.
Unlock the Tau Armor.
Unlock the Mu Armor.
Unlock the Psi Armor.
Unlock the Omega Armor.
Obtain the Spinner.
Clear every dimension.
Complete the game.
Obtain every treasure.
Score 25,000 In Score Attack Mode.
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.
Beat a boss without taking any damage.