To find the 4 Secrets in PC TNT level 16, Deepest Reaches:

When you first appear on this level, you'll be in a chamber
on the north edge of the map, facing south towards a closed
door in the far wall.
Go through the door and you'll be looking out across a pond
of crusted lava below you.  Continue a few paces forward to
stand at the edge of the pond, and turn back around to face
north, towards the door you just came through.
Just to the right (east) of that door you may notice that a
vertical band of the wall appears brighter than the rest of
the wall.  This marks the location of a tall secret door.

Secret 1: Activate that tall, narrow wall panel like a
switch and it will open, revealing a small chamber.  Step
inside to get credit for discovering a Secret.

Turn south again and run across the pillars to the opposite
side of the pond, and go through the open doorway in the
south wall.
Turn right and go through the door in the southwest corner.
Go up the steps and into the large room beyond.
In the middle of the room are some low, thick wooden walls
which partially surround a switch in the center.  Activate
that switch and the outer walls of the room will open up,
allowing access to a raised walkway that surrounds the room
on three sides.
Step up onto the walkway and go to the west side of the
room, where you'll find a switch in the middle of the wall.
Activate that switch, and go to the opposite side of the
room (east side), and through the new doorway you'll find
there.
Proceed southeast down some steps and into a low-ceilinged
stone cavern.  Continue forward to the east side of the
cavern, and turn left to face northeast.
Follow the running water north, then east, as it runs down
a long, narrow, winding stairway.
At the bottom of the watery stairway, turn right to face
south, and look for a teleporter booth in the southwest
corner of the room, and step into it.
You'll materialize in a tiny room on the south edge of the
east side of the map.
Step off the teleport pad and pick up the blue skull key
in front of you, then turn around and step back on that
same teleport pad you materialized on a moment ago.
You'll appear in the small room just south of the lava pond
near the map's entry point, and you'll be facing east.
Go forward, to a door ahead of you in the southeast corner
of the room, and go through it.
Head east across a short hallway, to an elevator/lift that
drops down automatically as you step on.
At the bottom you'll see a door; Activate the switch on
your right to open it.  Step through and turn left.
Follow the left-hand wall down the curving stairway, then
look for a blue-keyed door in the wall ahead on your left.
Go through this door and up the steps.  As you reach the
top of the stairs, turn right (east), and step southeast
into a short, wide curving passage.
A large section of the right-hand (southwest) wall of this
passage will open if you Activate it like a switch, and
reveal a small chamber.

Secret 2: Step into the newly-revealed chamber, and quickly
walk to the back wall (southwest wall).  Stepping into this
chamber will give you credit for discovering a Secret.
A long, narrow platform will rise up from the floor along
the southwest wall as you approach it.  On this platform
are some useful items, which become inaccessible once the
platform rises all the way up to the ceiling.  Grab them
now if you want them.

Step back out of this chamber, and turn left to face west.
Proceed northwest a few paces, along the edge of a high
dropoff on your right.  Continue a few more paces west
until you come to an opening on your left.
Step through this opening (south), and immediately turn
right to face west.  Walk a pace or two up to the red rock
wall in front of you, and turn right again, to face north.
You should see a passage that leads north/northwest.
Follow that passage until you come to a squarish opening on
your left, but don't step through yet.
If you look straight out this opening (northwest), you'll
see the flat face of a brown wall, which is across a gap
formed by a short dropoff in front of you.
That brown rock wall is actually a false, intangible wall
that disguises the raised opening of a secret chamber.

Secret 3: Step back a few paces, then Run northwest out of
the opening, over the gap below, and into/through that flat
brown wall ahead to gain access to the hidden chamber, and
get credit for discovering a Secret.
Some useful items can be found in this location.

Now simply step out of that chamber to drop down into the
gap/passage below.
Turn right to face another brown wall to the southwest, and
Activate it like a switch.
That wall is actually one side of a tall elevator that will
drop down when activated.  Step on and ride up.

Secret 4: At the top of the tall elevator is door.  Open it
and step into the small chamber ahead to get credit for
discovering a Secret.

The southwest end of the chamber is open, and looks out and
down across the lava pond near the map's entry point.

Done!

PC TNT players can click here to access a demo that shows
how to find all official Secrets on this level.