Is there a name for a war where everyone fights everyone else? I think that I heard the name "Kephyr" (Turkish? for the name of a war where it's all against all but I could not verify it.
"Internecine" is an adjective that carries some of that connotation. It can apply to either a conflict in which both sides suffer severe damage, or to an internal fight among factions within a group or a nation. Look it up and see if that's what you need, and choose your favorite pronunciation.
.. If you need a noun, you might try "free-for-all".