To kill the Cyberdemon on PSX Final Doom map 30, ONSLAUGHT:

General info:

A Cyberdemon can be killed with any weapon, if you have the
ammo, patience, and can survive long enough.  You can even
punch one to death, given enough time.
40 direct rocket hits can kill a Cyberdemon.  A BFG 9000 at
close range works well, too.  (In fact, if you can remain
facing him at point-blank range while the BFG completely
discharges, you can kill him with just 2 shots... But this
is not always an easy thing to accomplish.)

Specific tips:

The yellow skull key rests on a pedestal in the center of a
low platform, which in turn is surrounded by four pillars.
Get the Cyberdemon on one side of the pedestal, between two
of the pillars, and then move to the opposite side of the
pedestal.  Stand a couple of paces back from the pedestal
so that your feet are touching the ground, and are not on
the low platform.
The Cyberdemon will have a tendency to walk back and forth
between the two pillars, pausing now and then to fire at
you.  His rockets will strike the intervening pedestal and
explode, without hurting you.
In the meantime, you can use your rocket launcher and fire
at him... But the crucial difference is that your rockets
will go over the pedestal, where his did not.
You may instead wish to use a double-barreled shotgun, if
you have it.  Although it fires twice as many shells as the
regular shotgun, it hits 3 times as hard.
There's enough shotgun ammo spread around to finish off the
Cyberdemon with nothing more than that weapon.

You can also acquire a plasma rifle to attack with: If you
get past the Cyberdemon and explore around a little to
search out and Activate switches that you find, you'll get
to access a stairwell that drops down below ground level
for a few steps to go under a thick wall, and then it rises
back up to ground level with the next few steps.
At the middle of the stairwell, at its lowest point, turn
to the side and Activate the wall there.  That wall section
should lower, as well as the wall section behind you.  (If
it didn't, turn around 180 degrees to face the other wall
and try again.)
These two paths that open momentarily will allow you access
to the plasma rifle and some ammo.

Hope this helps. :)                                      

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