Please note that there are unicorns through this entire cave. Make sure to check after every battle to see if there are any unicorn horns. Pick them up to sell to Captain Argod in Krizsan.
Upon first entering head towards the north. In the northwestern corner of the first room is a passage containgins some Spiritual and Energetic Herbs. You need Move Mountains Lv.3 to reach them. Head towards the west, and then south until you reach a swampy area. There are some Healing Herbs on the ground here.
Continue going south and then west around the perimeter of the map. You'll be stopped just before the southeast corner by a Mossy Boulder and some Stalactites. Go back to the swampy area and head inwards toward the center of the map. Once you reach the basalt floor make a loop around, clearing out the unicorns. Ignore the lava pool in the center for now.
Once you've cleared the map, go back to the lava pool. There's a bubble at the northern end, which you can pop if you want. This brings forth a Demon, and I don't recommend this battle for beginners. Make sure to save your game before popping the bubble, and if you find you can't win this battle, just reload your saved game and leave, coming back when you're stronger.
Take any unicorn horns you collected to Krizsan, and while you're there you might as well tell Benedict the Armorsmith that you found Dominique and pick up your reward from him.