A fair bit of trivia for you. The Lethe River, in Greek mythology, is one of the five rivers of the Underworld and the river of forgetfulness, from which all dead souls returning to the world above must drink from. This is an ancient idea as to why no one can remember anything prior to their birth. (Though you, as a human (I hope), can't really remember anything before you were three or four years old, for your brain was underdeveloped before then.)
Anyways, another thing to note is Banon. For some stupid reason, if he is KO'ed, we can consider it a Game Over. So, if you want to be over-protective, switch him to the Back Row in a battle ASAP. Also note his technique "Pray". If you've played other Final Fantasies, you'll know that Pray heals the party's HP without MP cost. Abuse this EACH AND EVERY TURN with Baron; it's almost a full heal!
So, anyways, you'll go along the river for a while, fighting a few battles. Soon, you'll reach a fork in the path. You can go three ways here. Whichever you choose doesn't matter; going left just has less enemies. I don't recommend heading that way (why not have extra Gil and EXP.?). Soon past the fork, you'll reach a Save Point. Save there and get back on the raft. You'll soon reach another fork. Going "Up" provokes a loop; going "Left" allows you to proceed forward. You'll soon reach another Save Point so use it. Return to the raft and go along for a little while to find your next boss...
Ultros can use a basic attack, Tentacle (a powerful attack that can hit one person or everyone), and Ink (50% more damage than an attack and may inflict darkness). Specifically with Tentacle, Ultros will only attack one person (and often KO them) after a speech specific to that person. Who is attacked is obvious. However, Edgar doesn't get hit with single-target Tentacles. Why couldn't it have been Baron?
Onto the strategy. Baron really needs to move into the Back Row and use Pray each and every turn. Have Edgar use one of his Tools or resort to healing or reviving when needed. Let Sabin use his Aura Cannon Blitz if you have it (or, better yet, Rising Phoenix), and let Terra use Fire on Ultros. Just note that these latter two Fire-based attacks induce Ink counterattacks.
After the battle, you'll watch Ultros go back underwater and Sabin will chase him...