After following the corridor and going down to the first terrace, look for a small balcony on the left for access to a Codex Page and a Battery.
After the bridge, repeat with a secret hidden on a small platform underneath.
After a few aerial acrobatics, you will reach the central square of the area which is full of difficult fights and secrets. The Gore Nest that triggers an optional fight is very difficult in terms of timing since it conjures up a Doom Hunter. You should use the BFG-9000 or come back after retrieving the Crucible at the end of the mission, which will allow you to kill it in 2 shots.
There's also a button on the back of the statue in a small passage on the left, which will open the gate to the Master Token.
In the opposite corner of the arena, there is a statue that can be destroyed with a punch. Behind it there is another green button that will open the gate on the floor to the right. Break the chain to make the bell fall through the floor and reach the Battery.
To continue the progression, press the button on the back of the large central statue, which will bring up a basin with radioactive water. The principle will be each time to break grids with the dash in order to make the water level go down. Remember to check your radiation level.