This is what I suggest you do: Just run around that place and get the feel of the entire area. Use the map often. Once you do that...
You first have to go to the hot spring and touch the water, then go to the cave which is near the lower center of the entire area (I think) and talk to the purple woman (as nayoung said).
The poor girl gets really mad that you touched the hot springs and decides to fight you..
IN HER BATHING SUIT!!!Good luck on that battle, then get Alexander. He works pretty good against the one of the last bosses. And don't expect him to give you a revive skill anytime soon
!
edit: I almost gave something away!