How to defeat the Barons on level E1M8, Phobos Anomaly:

As you enter into the large pentagram-shaped room, two
side-by-side booths open to release a pair of Baron Of Hell
monsters.

Unfortunately you can't exit the level without defeating
both of these monsters.  However, they are by no means
invulnerable.  In fact, they can be killed by any weapon,
including your fist.  The only trick is hitting them more
than they hit you. ;)

First, make sure you have plenty of health and ammunition.
You'll find some stimpacks at the top of the elevator that
is located across the room from the level's starting point.
There is also a secret panel in the first long hallway...

Before entering the pentagram, you can find 2 weapons, and
some boxes of ammo, in the twin rooms off to either side of
the main corridor.
If you got a rocket launcher on an earlier level, so much
the better: five or six direct rocket impacts will kill any
Baron.

When you face the Barons in combat:

One of the most valuable skills in Doom is being able to
"Strafe" (or side-step) to avoid enemy projectiles.
(In PC Doom games, Strafing is typically done by pressing
the "<" or ">" keys, or by holding down an Alt key while
pressing a left or right arrow key.)
Practice this technique if you're not used to it.  You'll
need this skill here, and even more so in future missions.

You can defeat the Barons by simply keeping your distance
from them as much as possible (if they start getting too
close, run to another part of the pentagram), and direct
continuous fire at them, while dodging whenever necessary.

Other tactics you can use:

If you can lure the Barons near, or into, the cluster of
barrels and then detonate them, the Barons can be hurt;
sometimes significantly.

(See the E1M8 demos, for more tips on using the barrels.)

When playing at higher skill levels, there will be Spectres
(semi-invisible Demons) in the pentagram room, as well.
If a Spectre gets hurt by a Baron's fireball it may turn
and attack (and possibly distract) the Baron.
You can try to use that fact to your advantage by allowing
Spectres to occasionally come between you and the attacking
Barons.  (Just make sure not to get pinned into a corner by
more Spectres than you're ready to take on. ;)

Another tactic in PC Doom games is to try and lure the
Barons around to the far/north side of the wide stairway
that leads up to the twin booths.  Once you've done this,
quickly run back to the south side of the stairway, and
stand on the lowest part, next to the elevator.
From here, you can fire at the Barons and hit them, but
their return fire will be unable to reach you, striking the
north edge of the stairway instead.

Finally, you can try using the Blur Artifact (or "Partial
Invisibility" sphere) in the west corner of the pentagram.
When this Artifact is in effect, the Barons will have a
harder time throwing fireballs straight at you.  (However,
this may or may not be helpful, depending on how close they
are to you, and how instinctive your dodging reflexes are.)

To read about and/or download some combat demos for this
level, click here.