Grey Prince Zote is an optional boss that can be accessed in Dirtmouth after doing the following:
1) Rescue Zote in both Greenpath and Deepnest.
2) Complete the Trial of the Warrior in the Colosseum of Fools, defeating Zote as the final boss.
3) Acquire the Monarch Wings (obtained after defeating Lost Kin in Ancient Basin).
4) Rescue Bretta from Fungal Wastes so she returns to Dirtmouth.
5) Acquire the Dreamnail from the Seer.
Once all this is done, Bretta's house will be open in Dirtmouth. It's the far right structure closest to the well. Enter and you can access the basement where you'll see a statue of Grey Prince Zote. Strike the statue with the Dreamnail to be taken to a new area where the encounter will begin.
Note that since this is a dream encounter, dying just takes you back to the Bretta's basement without penalty; fragile charms will not break.
Defeat Grey Prince Zote and the achievement will unlock (and you will receive 300 Essence).