How to beat the Cyberdemon on level E2M8, Tower of Babel:

This level marks the appearance of Episode 2's Boss, the
Cyberdemon (or "Cyber Demon", "Cyber-Demon").

For better or worse, you must kill the Cyberdemon to exit
this level.
However, this monster is by no means invulnerable.  In fact
he can be killed by any weapon, including your fist.  The
only trick is hitting him more than he hits you. ;)
40 direct rocket hits, for example, can kill a Cyberdemon.

There is a rocket launcher and plenty of rocket ammo in the
4 rooms that surround the central chamber where you begin
the level.  You can also find a few other useful items in
those rooms.

Note that once you open an interior door (leading out to
one of the 4 rooms) and step through, it will close again
automatically behind you.  A closed door cannot be opened
again from the outside.
If you wish to get back inside the central chamber, it's
advisable to keep at least 2 interior doors open at all
times.

Techniques for combatting the Cyberdemon:

One of the most valuable skills in Doom is being able to
"Strafe" (or side-step) to avoid enemy projectiles.
Practice this as much as possible if you're not used to it;
you'll need this skill here, and in future missions.
("Strafing" in PC Doom games is commonly done by using the
"<" and ">" keys, or by holding down the Alt key while
using the left or right arrow keys.  Details on the strafe
function are in your Doom game manual, or press the F1 key
during a game for a list of commands.)

The Cyberdemon can be killed by keeping your distance while
firing at him, and dodging whenever necessary (if he begins
to get too close, run away from him and/or get a pillar or
wall between you).
Note that a Cyberdemon typically fires in 3-rocket bursts,
sometimes pausing and/or moving before firing again.

There are also some other tricks and techniques that can be
put to use on this map:

The narrow-gap advantage: There are narrow vertical gaps
between the main building and the very large blocks at the
four outside corners of the main building.  Rockets can't
pass through the gaps, but rocket explosion effects, and
some other projectiles, can.
If the Cyberdemon is on the far side of a gap, his rockets
won't pass through, but your bullets and shotgun pellets
will.  (The secondary invisible rays that emanate from a
BFG weapon can also pass through these gaps.)
Be careful not get too close to the gap during a firefight,
as explosions from his rockets (and your own) can hurt you.

The switch-post trick: With a little luck and skill, you
can maneuver the Cyberdemon into one of the four rooms
surrounding the central chamber, and get the post/pedestal
of four switches between you and him.  If you position
yourself correctly, your rockets will go over the switch
post and strike him, while his will strike the post and
miss you.
You'll have to stand at a spot where your back is against
the door (or open doorway) of the room opposite the one
he's in.
Be careful not to step too far back, through the doorway of
the room behind you, or your elevation will change and his
rockets will be able to clear the top of the post.
If you need to gather ammo, be sure to leave a door or two
open when you leave the central chamber, so you can get
back in later.

To read about and/or download a demo of a strafe-and-dodge
victory over the Cyberdemon, click here.
To read about and/or download a demo of a victory over the
Cyberdemon using the rocket/switch-post trick, click here.