'The End of the Cycle' is the achievement for rejecting an offer at the end of Realm VI. You will need to unlock the Roots of Chaos first. Here are the steps:
1. Beat the main game by defeating Kriterion in The Old World (Realm V).
2. Deny Kriterion’s judgement.
3. 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.
4. Make sure you also have the skill ‘Ground Pound.’
5. At the very left of the Chiming Tree, use ground pound (jump, then RB + down) to dive into the water.
6. Swim to the portal to see the ‘Roots of Chaos.’ Double-check the very top diamond 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.
7. After beating world VI's Judge, an entity will offer you a choice. Reject it and give up your power.
Accepting the offer instead grants the other achievement 'The New Vessel.' Getting both will require two separate runs.
***NOTE: As of 26 Oct 2020, 'Invulnerability' does not actually disable achievements in ScourgeBringer! Go to ‘Accessibility’ in the options menu and change HP regen assist. This may be patched out later.***