10 minutes is really quite easy even if you haven't leveled up as long as you do a couple of things.
dont draw or or explore the fire cavern too much. proceed to ifrit asap.
when fighting Ifrit, dont cast quezacotl. have some one cast shiva and the other person attack; casting both GFs wastes too much time. its also preferable that Quistis is the one with Shiva, as Squall's higher str will be needed for his attacks.
anyway that should do it.

you can level up/draw/explore after Ifrit is defeated, as the time limit goes away.