Go down the narrow corridors , eliminate spawns that appear , and perform a wall run. You should reach a new room with an inactive statue in it (missing lantern), and since can't do anything yet in here, go through the Northern door. After you get in a new corridor, look around for edges shown in the above screenshot, and start climbing.
Shimmy to the right and wall run towards the vertical wooden pole. Lean back and jump back now, and will run towards the upper ledge where there is a unique weapon there - Lich Spines. Jump down now and resume your march towards the northern room.
The puzzle that you can find in this room that consists of several parts. Position the death anywhere you want and use Soul Split. Start operating the mechanism, shown in the above screenshot, will with the first part of the soul, which will bring down a large grate.
Press and hold down the E key in order to change controls over to the other half of the soul (the other one needs to hold the mechanism in order to prevent the grate from coming up. Go to the unlocked part of that room and find the place in which you can use the death grip to catch a shadowbomb. Return with the bone to the place where you started, and toss it towards the switch visible on the above screen.
[TIP: using death grip does not stop the activity of the Soul Split, because those skills are independent from each other.]
Notice that hitting the switch with the bomb coast unlocking a small niche in which there is the small platform shown in the above screenshot. Approach it (keep controlling the second part of the soul at all times) and tried it towards the starting place.
Return for a moment to your physical form, but only in order to step on the platform (the above screenshot). Make sure that that death stable on the platform and him. We went use Soul Split again.
The first half should go and use the central mechanism again and bring the grate down again. Switch it then to the other half of the soul and start pushing the platform on which there is the physical form of the death located (the above screenshot). The plate needs to be pushed over to the other side of the grate. Once done, terminate Soul Split.
Remain in the eastern part of the room for a moment and turn your attention to two pressure plates around. Position the death of one of them and initiate Soul Split. Use the first part of the soul to approach the other pressure plate. Switch over to the second half now, and go towards the unlocked chest (the above screenshot).
Return to the physical form, now, and use the only available passage. After you reach a forking, choose the northern stairs. After you reach the balcony, deal with spawns and examine the contents of yet another chest. Now, return to the forking and jump into a small hole shown in the above screenshot.
[TIP: if you jumped into the hole right away, unfortunately your way to reach the chest will be more difficult. If you do that you have to pass through all of the locations that you already explored and once again do the puzzle with the grate and the pressure plates.]
Sneak a peek into the nearby chest, and go South. Here you'll find another one. Inside the chest, you will find a Skeleton Key (the above screenshot). Take the key with you and here's nearby switch, in order to unlock the access to the central location visited before.