Here is the full list of all 16 ARKOS achievements.
Escape from the river of lava on E1M03
Kill 100 enemies
Collect 50 big mana potions
FInd 20 secrets
Master the teleport power
Kill 500 enemies
Break 100 objects
Pass the level without damage
Kill 1000 enemies
Collect 50 big health potions
Find a secret scroll on E1M03
Find a secret scroll on E5M01
Сross the level boundary on E2M01
Find a Dopefish on E2MXX
Find a secret portal on E2M03
Find insane difficulty portal in a Hub