After failing in your first attempt to control the netherbrain with the stones, the Emperor will save you by pulling you back into the astral Prison. He will suggest that he come with you and use the stones, but he’s pretty weak, so suggest you become a mindflayer yourself. He’ll tell you to talk to your companions about it first. Most will be against the idea. Karlach will suggest herself to become a mindflayer instead of you. Ignore them. Become a mindflayer and complete the game, killing the netherbrain.
However, as a mindflayer, you lose some abilities. Your strength and dexterity drop to 13, and your Intelligence and Charisma become high. As a mind flayer, you can use bonus actions as actions and vice versa. A build like thief 3/wizard 9 will make great use of these changes, while a pure barbarian will be nearly useless. Thus, if you plan on this achievement, before you get in the boat, talk to Withers and change your class. The Thief rogue’s two bonus actions are fantastic for mindflayer PCs. Other good builds include:
Frontliner: Fighter (Eldritch knight)3/ Thief 3/ Warlock (blade) 6
Healer: Thief 3/Bard (lore) 9
Caster: Fighter 1/Wizard 11