Celes and Sabin join Edgar in cleaning out his clogged-up engines. Each Tentacle has different elemental absorbs and weaknesses, so this fight can be really drawn-out. Furthermore, the Tentacle's favorite tactic is to use Entwine or Stun on the party to inflict them with Slow status. If anyone is slowed, a Tentacle will then Grab them and remove them from the fight while draining their HP. It takes thirty seconds for anyone to be released from a Grab, making the battle even lengthier.
The trick is to equip Sabin and Celes with Hermes Sandals. Having auto-Haste makes the character immune to Slow, and anyone who can't be Slowed can't be Grabbed. You're then free to use magic or physical hits to take the Tentacles out one by one.
Edgar autoequips your best weapon, shield, and armor when the fight starts, but you can't access his Relic equip screen, so he tends to get Grabbed and drained and there's nothing you can do about it.
Two of the Tentacles (top-left and bottom-right) are vulnerable to Petrify, and the bottom-left one is vulnerable to instant death. Knowing that at any point in the last twenty years would have let teenage R^2 approach this battle with rather less apprehension.
It's a difficult battle, but if you can keep two party members from being Grabbed, it's winnable. Having all three party members in the Tentacles' grip is a good way to lose, though.
Edgar: I'd heard Figaro had run into some kind of trouble. I wanted to help, but how was I supposed to get here with the castle stuck beneath the sand? Then I caught wind of the rumor that those guys had escaped from the dungeon...
Celes: So you used them...
Edgar: Bingo. And obviously, I couldn't let them find out I was the king of Figaro...
Celes: ...Because they'd just escaped from your own jail.
Sabin: You could've told us.
Thief: That monster must've gotten him...
Henchman: Poor boss... didn't even last as long as the last boss...
Robber: Oh well... Let's go.
Edgar: I couldn't care less about treasure. What we need to worry about is Kefka. Those guys haven't done anything wrong... not really.
Celes: So... you'll come along?
Sabin: Let's go shake things up again!
And Edgar joins the party!
The thieves may have swiped everything from this vault, but they didn't notice that the sword stuck to this statue isn't purely decorative.
Hmm. Turns out Edgar wasn't ever in the party when I had espers equipped to people. He doesn't know a single spell.