Chaos is an extra “challenge mode” that you can unlock after beating Kriterion in the main game. See below for the process. You can skip step 1 if you want to play legitimately, but I recommend achievement hunters take advantage of accessibility mode to get most achievements in just a couple hours.
1. Go to ‘Accessibility’ in the options menu and change HP regen assist to ‘Invulnerability.’ This will NOT disable this achievement. -- (I tested on 26 Oct 2020.)
2. Beat the main game by defeating Kriterion, Herald of Judgment in The Old World (Realm V).
3. Deny Kriterion’s judgement.
4. Press ‘continue.’ At The Chiming Tree (home base), run left to the skill tree altar. Scroll up to see the new skill ‘Truth Seeker’ available for 35 judge blood. You may need to farm a few more mini-bosses, judges, and blessings.
5. Make sure you also have the skill ‘Ground Pound.’
6. At the very left of the Chiming Tree, use ground pound (RB + down) to dive into the water.
7. Swim to the portal to see the ‘Roots of Chaos.’ You now need to select modifiers to add up to at least 5 chaos (of a possible 17) in the top right. I recommend ‘Max HP,’ ‘Oppression Challenge,’ ‘Escalation Challenge,’ and ‘HP.’ You will be invulnerable, so there is no need to have high max health or heal at all. The other options have potential to slow you down, like by making enemies stronger.
8. Make sure the very top diamond still says '6- The Truth' then press B to start the ordeal. You will now run through the main game again, but after beating Kriterion there will be a sixth, space-y world. I recommend speed-running the levels as fast as possible because you have no need to find bonuses and store up blood when there's not a chance of dying.
9. Clearing this world's Judge with your total of 5 chaos will net you ‘The Seeker of Power’ (for beating the mini-boss), ‘The Beyond,’ ‘Embracing Chaos,’ and ‘Being Chaos.’ Your decision at the end will also earn either ‘The New Vessel’ or 'The End of the Cycle.'