One day after completing Spider Cleanup, you'll find an event on the world map leading to a battle and meeting a new character named Edwin. After the event, you gain entrance to the Congregation building. Entering the building for the first time triggers the quest.
First, you need a rope to descend the chasm in the northern mines. Once that is done, you get in an area containing a stone door. This door leads to the vault. On the west wing of the area, a lever allows you to open the door. If you don't use this lever, you have to destroy the door to progress.
Inside the vault, you'll have to reach the domain to progress further. The domain is behind a gate and said gate is guarded by a minotaur.
Three paths allow you to reach the minotaur:
Each of the two wings of the vault also contain a miniboss guarding an orb. Those orbs can be placed in slots close to the gate guarded by the minotaur. Once the two slots are filled, the gate opens, and you don't need to destroy it.
The minotaur follows the following action pattern:
One possible strategy to counter this is:
Now that the minotaur and the gate are dealt with, you just need to open the domain. Learning Open Domain I requires to meet a 20 MP requirement. The Mana Capacity lesson in the spellshop helps a lot to meet the requirement.
Inside the domain, you can now fight the low-demon. This boss is really hard without proper preparation. If Aura has higher AGI than John and has Tailwind set up, there is a strategy allowing you to reliably defeat the demon without removing Aura's collar though:
After defeating the demon, the last step is just to report to the guild.