You could always get lucky and hope that it doesn't use the Bubble attack, thought I don't know if that would help or not.

When I did that part, I had Cloud with Meteorain, so...I don't think I can help much.

Well, at least there aren't many monsters like these that will give you trouble, except for the Demon's Gate. Luckily Yuffie's limits cause alot more damage then Cait's.

Things you should always have on:

Enemy Skill (Learn Trine/Aqualung/Beta, Big Guard, and White Wind as soon as possible).
Counter-Attack
HP Plus, MP Plus optional
Elemental Rings/Ribbon depending on your enemy
Time Materia

There's probably some others, but these are some of the best selections for a solo challenge.