This article is from the Final-Fantasy and other Square Soft Games FAQ, by firstname.lastname@example.org (Nick Zitzmann) with numerous contributions by others.
C. Armor is tricky, because he actually consists of three parts, the
left and right arms, and the main body. C. Armor has the ability to pick
up your allies and hold them there. This is bad because damage inflicted
on the arm holding an ally will also hurt the ally. Even worse, if he's
holding an ally and the other(s) are killed, the game is over!
Since C. Armor and its components are weak against Lightning, use
Bolt-based spells and attacks. Work on taking out it's arms before going
after the main body. The Phoenix materia and Life spells come in handy
here as you will need to revive your allies more than once, presumably.
Also, keep your HPs high, as the main part of C. Armor has a deadly
attack called the Lapis Laser, which causes around 1500 points of
damage! I suggest using Big Guard, or at least Barrier and Haste, in
order to protect yourselves.