In the room with the red keycard drop down to the ground, go to the southeastern corner and push the switch on the balcony's eastern wall. Go through the white teleporter to get back to the balcony. In the area right south of the balcony a platform with a soul sphere has lowered (#1).
From the blue key-lock area, head north and you will be outside a window with several large windows. Enter this building from the southeast to open a door upstairs containing a soul sphere. The door will close on you as you try to approach it. To get this soul sphere, walk out the window right behind you with the door closed. You will then have to strafe run up the stairs, such that you trigger the mechanism that opens the door, but that you cross the mechanism that closes the door before the door is fully opened. If you are successful, the door will remain open and you can enter the room with the soul sphere (#2). A much easier alternative way: Simply trigger the door to open and leave the hallway through the southeastern window again, thus leaving the door opened and simply teleport next to it without closing the door: On the plasma gun balcony (see secret #3) open the western wall to find a white teleporter. Use it to reach the soul sphere.
After opening the door with the red keycard and walking all the way around the elevated walkway through another small door, turn left. On the left is a highlighted wall with pipes on it. Open it to be teleported (#3) to a plasma gun and a medikit. The red teleporter leads to two bullet boxes and a box of shotgun shells, along with two chaingunners. Push the wall with pipes on it next to the shell box to open up a shortcut back to the hallway where you found the first teleporter.
In the room in the north part of the map with many stacked crates, walk to the top of the stack in the southwestern corner (on the way to the blue skull key). Turn around and run onto the crate with a squarish light in the middle, then run to the box on the right (#4) to get a soul sphere.
If played in Cooperative, this level may become impossible to finish. If one of the players crosses the trigger behind the blue door (Linedef 2284) which makes the blue skull marked bars behind him to close, and dies inside that room, the level will become impossible to finish due to the only trigger to reopen the bars is a switch in a room following the blue key door (Linedef 2635).