This is unlocked by 'failing' the game - which is done by letting the Doom Counter increase to 10+1. When you open your inventory, in the top right corner, you'll see a symbol with circles around it. This is the Doom Counter. A filled-in circle means you're at/past that level, so 5 filled in circles means Level 5 essentially. There are 10 circles, but you won't fail until it goes 1 level past the 10th circle, hence 10+1. This was surprisingly difficult to accomplish.
The Doom Counter seems to semi-randomly increase after story missions. However, it consistently increases after every 3rd faction quest completed. Just keep completing them without lowering the counter and you'll get this. You can abandon faction quests with 0 consequences if you want to re-roll available quests.
It's a good idea to make a save to fall back on (I didn't want to play at a high Doom Count or have to lower it when I was done).
Then, just keep doing faction quests - the Memora ones are probably the easiest, but there is an exploit that can be used on the Ripper Pome quests.
Gather some Ripper Pome from a lower dungeon (I had 12), then return to Upper Erebus. After accepting the quest, find a safe spot and make sure you have a hotbar slot open. Transfer 1 Ripper Pome to your hotbar and then drop it. Drop 5-6 this way, and then pick them back up. It'll count towards the quest and let's you basically auto-complete them. Eventually, it'll stop working but it's helpful for a few quick completions.
GLITCH WARNING:
I would recommend doing this in one dungeon & in one sitting. Seemingly randomly, the faction quest board will be blank after going through a loading screen. At first, I assumed that at a certain Doom Count, they were unavailable. However, the board just either glitches out or it's random if there are quests available. If it's blank for you, try going to a different dungeon. Sometimes, saving/re-loading the game worked as well. If that still doesn't work, try taking a portal back to Marcaul, restart the game, and then check the boards again. Make sure to check multiple dungeons. Eventually, you'll find that they become available again.