No biggy.

The main point is, however, that this challenge is nearly impossible, if not completely so.

The only usable healing abilities you have are Yuffie's and Aeris's healing Limits. Both have the same requirements in terms of HP loss required to Trigger (66.4% of max HP). After Aeris dies, Yuffie is your only source of healing. If she isn't in Fury status, her healing won't be able to keep up with the damage the party takes. If any other party member is attacked more than her, they'll die and won't be revived until an in-game event.

If it is possible, it's just a question of luck, nothing more. It's a rush through to the game until you can find an enemy who puts you in Fury status, and then it's just a question of grinding and resetting if the wrong character is attacked or your healer is knocked out of Fury status (or any character takes too much damage in a single hit).