To be able to access the area necessary for this achievement, one will need a Bloody Writ. These can be earned after desecrating a sanctuary that doesn’t belong to one’s existing creed and, then, dying to the waves of enemies that follow. To do that, use a Stained Page in the desired sanctuary.
Note: Per Gunblade44, rest at the sanctuary you plan to desecrate, otherwise you won’t earn a bloody writ.
Assuming one has a Bloody Writ, follow these steps.
1) Start at the Siam Lake sanctuary and go right until you reach a hole with water leaking down; you’ll likely want one or two torches and there is one cave keeper in the area
2) Fall down the hole, then continue to fall using the side the water is falling off of the platform as a guide. The pattern is left, right, right, right, left, right, right, right.
3) With the very last drop, jump far to the right and use the air dash to clear some extra distance (there is a breakable floor at the bottom of this section that will easily kill an unsuspecting adventurer while stunned from the big drop).
4) There will be an individual dressed in a black getup at the bottom. Talk to him, offer the Bloody Writ, and answer ‘yes’ that you “wish to swear your blood to Him.”
5) You have joined the Order of the Betrayer! You can use the newly acquired key to progress further to the right and find a new sanctuary