As you enter note the skeleton key door opposite and the socket on the floor. Now climb the stairs. At the end of the northern balcony there is a hanging switch. Enter soul splitter and have clone 1 activate the switch. This will open the door on the southern balcony. Drop down the hole inside and follow the pathway at the end, climb the wall.
In the room at the top; pull the ball over so that it is next to the pressure plate and facing the locked circular passage to the south. Stand on the pressure plate to lower the gate and punch the ball down the hole. Exit soul splitter and cruise on open to the now open door. As you enter, look around behind the stairs you came in from to find a chest.
Then make your way to the south of the room. When you reach the gap, look up to your left to see a stone block we can wall run up to, do so and use deathgrip at the end to jump up to top of the structure in the centre of the room.
Exit soul splitter and then re-enter. As with the last bit, get both clones back over to the hanging switch. This time have one wall run over to the left until he reaches the handhold here. Now have the second clone wallrun to the handhold to the right. Switch back to the first clone and use the deathdrip rings and wall blocks to continue to the left and make your way over to the platform at the end.
Rotate the lever here so that the bridge moves 90 degrees. Leave the clone holding the switch and change back to the second clone, have him work his way down to the ball and push it across the bridge into the socket. Grab the skeleton key from the chest inside the room that opens. Exit soulsplitter and look off of the central platform to find a pipe, drop down into this for a chest and then return to the previous room.
Open the skeleton key door and follow the passage inside to the circular room at the end. As you enter, a gate will drop and you'll have to fight off a group of forge guardians. Once they are all dead, you can loot the chest.