My advice would be to have one character hang back, and for this singular reason:

Firemane (or whatever it is called) has a notable attack that covers a wide area, damaging all of your party within its range. Having one character hang back (I used Fran since she has a respectable bow) allows you to both survey and anticipate the next move(s) made by your enemy.

I made it through with being levels 7 and 8, so it's most definately not impossible or difficult to do.

This Final Fantasy hails status manipulation, so be sure to watch for such things as they will basically tear you apart. And watch your health like a hawk: taking the MP and time to heal a character when they are around half life is much easier to do than when two of your characters are low in health or dead.

You're going to want to rush the battle, and I know I felt a little panicked and frenetic during the first boss battle, but really, it seems to work best to take things slower than you think they ought to be.

And, obviously, do not cast Fire elementals on it. If you happen to have Water or Ice, use such things.

Libra (which you can cast far before engaging battle) is most definately useful as it shows the enemy's health and weakness(es).

Hope that helps.