How to get to the Soul Sphere and Mega-Armor on level 11,
Terror Core:

Step outside the starting room, and turn right.  Ahead of
you, in the corner, is a small alcove in the wall, where
the blue key will appear.  First, you have to kill all the
monsters in the open area around you.
After defeating the monsters, go back to the level's entry
point.
Follow the right-hand wall, walking past the alcove, and
continue counterclockwise around the courtyard, under two
bridges.  Continue under the next right-angle overpass on
your right, and follow the right-hand wall to a covered
stairway behind a diagonal wall.  Go down the stairs and
Activate the two switches you'll see ahead in the corner.
Now go back and get the blue key which has appeared in the
alcove, and use it to open the blue-keyed door that's just
across from the starting-room door.
Go up the first few steps, and at the 4-way intersection,
turn left.
Go up the stairs to the door and open it.  Go through and
take a U-turn around to your right.  Follow the path along
a right-angle bridge, until you come to the entrance of a
large room.
You'll see a switch on the wall ahead of you in the middle
of the room; Activate it.
Go back along the right-angle bridge, and when you get to
the end, turn right and go up the stairs, past a 3-column
barrier that drops when you approach, and go past it into
the courtyard beyond.
At the opposite end of the courtyard, in the middle of the
long wall, is a switch nestled between two curved, raised
platforms.  Go Activate it.
While you're here, be sure to kill any monsters that are
wandering around in the courtyard.
When all the monsters are dead, the 3-column barrier drops
down again, allowing you access to the stairs you came up a
few moments ago.
Go back down the stairs, and at the bottom, take a wide
U-turn around to the right.  You'll come to an elevator;
ride it up to the top and step off.
Go through the door ahead and turn right.  Go through this
door and run across the short bridge into the next chamber.
Turn right and go through that door, and across another
short bridge, to where you'll find a switch on the wall.
Activate it.
Turn around and go back through the door.  Turn left and
go through the door and across the bridge through the next
door.
Go past the door on your left, and continue straight, down
another bridge, to where you'll find a teleporter ahead and
to the right, in a corner.
Step into the teleporter, and you'll be sent to a platform
at the edge of the courtyard where you were a few minutes
ago.  When you appear, the yellow key will be at your feet.
Pick it up, but don't step off the platform just yet.
As you pick up the yellow key, turn right to face a switch
on the wall across from you.
Back up against the wall behind you to get a running start,
and then Run (remember your Run button) to jump to that
switch, and Activate it just as you smack into it.
This can be very difficult to do, and may take several
tries.
Once you've activated that switch, a secret doorway opens
up, just across from the teleporter that took you to the
yellow key.
Go into that secret doorway and follow the curving tunnel
around to a door.  Open it and step out on to the platform
ahead.
Turn right, and you'll see the Soul Sphere on another
platform, diagonally across from the one you stand on.

To jump to the Soul Sphere you'll want to use a combination
of Run plus Strafe, which yields a speed slightly above
that of plain running, but moves the player character at an
odd angle.  Here's one way to do it:
Turn to face the Soul Sphere, and then back up, to put your
back into the corner behind you (just to the left of the
door you just came through).
Note that to the left and right of the Soul Sphere, you'll
see two bridges.
Select your pistol, and turn a little to the left, to point
your pistol at the left-hand bridge.  Aim your pistol at
the left end of this bridge.  This will rotate you to a
good angle for strafe-running to the platform.
Hold down your Run button, and while it remains held down,
simultaneously press both your Forward button, and your
Right-Strafe button.  (By default, "Right Strafe" is the
rectangular button at the right edge/shoulder of your game
controller.)
Hold all three buttons down until you've landed on the
platform where the Soul Sphere is.

When you have the Soul Sphere, step down off the platform
to land in the courtyard below.
Go back down the stairs, and at the bottom, take a wide
U-turn to the right.  You'll come to an elevator; ride it
up to the top and step off.
Go through the door ahead and turn right.  Go through this
door and across the short bridge and into the next chamber.
Open the yellow-keyed door and go through.
Go across the bridge and into the tunnel, turning right and
going down the long stairway.
At the open area at the the bottom of the stairs, look to
the right for the red key, and grab it.
Turn and go back up to the top of the stairs.

Note that along either side of the stairway are raised
ledges.  At the top of the stairs, as you look down towards
where you got the red key, note the left-hand ledge.  At
the far end of this ledge is a panel in the left-hand wall,
which opens when you cross a trigger line.
Switch to your wireframe Automap view (view 2), and look at
the top of the stairs, where the tunnel makes a right-angle
turn.  You'll see a yellow line that runs diagonally across
the floor here; This is the trigger line.  When you step
across it, that wall panel at the far end of the left-hand
ledge will open up momentarily, and then close.
You'll want to get to that panel and go through before it
closes.  Here's one way to do it:
Walk a pace or two down from the very top of the stairs, so
that the yellow trigger line is just behind you.
Now, Run backwards across the trigger (opening the panel)
until your back hits the wall behind you, and quickly
side-step to the left to get on to the ledge, then Run to
get to the panel before it closes, and go through it.

The panel opens to a small, empty chamber.  Once you get
inside, turn around to open that panel again.  Now back up
to get a running start, and Run across to the ledge that's
on the opposite side of the stairway.
Turn right and follow this ledge to an open doorway in the
wall on this side of the stairs.
Go through into the tunnel and follow it to a door.  Open
it and step on to the platform ahead.
Turn right, and you'll see the blue Mega-Armor on another
platform, diagonally across from the one you stand on.
To get to the armor, use the same "Strafe-Running" maneuver
that is described above for accessing the Soul Sphere.

Once you have the armor, step down off the platform to land
in the courtyard below.
Go back down the stairs, and at the bottom, look for a door
just ahead and off to the right.
Go through and across the short bridge, and down some steps
to a 4-way intersection.
Turn left in the intersection and go up the steps to get to
the red-keyed door.
Go through the door, and as you step across its threshold,
a barrier will drop nearby, around the corner to the right.
The barrier stays down for a moment, then rises up again.
When the barrier is down, you can access a teleport pad on
the floor.  Step on to be sent to the exit area.
When you appear, the exit switch will be behind you, on the
other side of a partition.