How to get to the keys in level E4M2, Perfect Hatred:

First, you need to get to the lava pool in the large room
just to the west of the level's starting point:
When you start the game, Run up and off of the left-hand
stairway, to land on the west-side platform ahead of you to
the north.  (In PC Doom games, "Run" is typically enabled
by holding down the Shift key.)
To your right is a pillar with a switch on it.  Activate it
to open a door high up in the west wall, behind you.
Run west off the platform you're on to jump through that
new doorway in the wall.
Just inside and below that doorway is a small platform,
down in the lava pool that covers the floor of this room.
Drop down to that platform.
Just to the north of that platform is a small triangular
area of the corrosive floor.  (On Skill levels 1, 2 and 3,
there will be a radiation suit here; on Skill 4 or 5, it
will be missing.)
If you step into this triangular spot, a narrow section in
the middle of the north wall of this room will rise up,
revealing a stairway that leads up and north.
Step into that triangle, and quickly step back onto the
platform.
Next to you, at the east end of the platform, is a switch
on the wall, located just under the raised doorway you came
through a moment ago.
If you Activate this switch, a walkway will begin to rise
out of the floor.  This walkway will extend all the way
around the outer edge of the room.
Activate the switch, and, if you move very quickly, you can
Run south to get on the walkway as it rises.
(If you didn't get on the walkway in time, leave this room
by going north up the stairs, and Run for the red teleport
pad you'll see on the floor ahead of you to the north.  It
will take you back to the level's starting point.)

Once you're on the walkway, follow it clockwise around the
room.
You'll come to a small gap in the walkway.  Run east to
cross that gap to a widened area ahead where you'll find
two green torches.
As you step into this area, a part of the back wall will
open up, revealing the yellow skull key on the floor of a
small chamber.
Pick it up, and go back to that gap in the walkway.  Drop
down into the gap and turn north and go up the stairs
ahead.
You'll see a red teleport pad on the floor, several paces
ahead of you to the north.  Step on, and you'll be sent
back to the level's starting point.

Run up and off of the right-hand stairway, to land on the
east-side platform ahead of you to the north.
To your left is a pillar with a switch on it.  Activate it
to open up another platform ahead of you to the north.
Run to get across the gap to that platform.
You'll see that a part of this platform narrows and extends
off towards the northeast.
Run northeast to land on another narrow projection which
continues northeast to a large, irregular room.
Enter this room, and continue southeast to drop down off
the platform you're on.
Proceed south around the various obstacles and look for a
stairway in the middle of the south wall.
Follow the stairs up and around, and you'll see a teleport
pad ahead of you.
To the left of the teleporter is a small chamber to the
south.  The blue skull key is here on the floor.
The teleporter will return you to the level's starting
point.

To access a downloadable demo which shows how to acquire
the keys on this level, click here.