Once you've entered Figaro Castle, cross over to the engine room and descend the stairs that were previously blocked. You'll find yourself in Basement 2. The Encounters hwere are the same as they were in the Secret Path in the South Figaro Cave. There is nowhere to go but north, where you'll find stairs leading to Basement 3. Here you'll encounter the same Monsters as in the first part of the South Figaro Cave, which means you'll start seeing Dantes again. You'll also find a large number of Figaro Castle guards lying on the floor. You can check on them, but none of them tell you anything useful.
Follow the available path south where you'll find a room with three northern doors and two southern rooms. You can obtain a Gravity Rod and Crystal Helm from the chests in the eastern room, and an Ether and an X-Potion in the western room. The Crystal Helm is an improved version of the Diamond Helm and may be worth equipping to Celes. The central door to the north leads to the end of the dungeon, while the western door leads to some stairs and eventually a Regal Crown. This is a powerful piece of headgear usable only by Sabin and Edgar, and may also be worth equipping now.
When you enter the Engine Room, you'll see Gerad and the Crimson Robbers. Speaking to Gerad triggers a series of events that culminates in Edgar (surprise!) joining the party for a boss fight against 4 Tentacles. You may be attacked by three Drops in here. All they do is use Mad Signal to inflict Muddled, and counter Fight with basic attacks. You can use Thunder to easily defeat them.
Tentacles
This boss fight is a side attack. Edgar automatically equipped whatever was available, which is nice. The four Tentacles each have different vulnerabilities and HP totals, but the same attacks. The top tentacles have no weak points, while the Bottom Left and Bottom Right are weak against Fire and Ice, respectively. Consult the sidebar for a quick reference. The Tentacles also have varying Status defense.
The Tentacles' main attack is Seize, which takes a Character out of combat for some time and repeatedly drains them of HP. This is used against Characters with the Slow Status, which is usually inflicted with a different attack also called Seize. As a result, RunningShoes make the wearer immune to Seize. Edgar has no Relics equipped, so he'll be vulnerable in any case. After about 30 seconds of HP draining, Discard will be used to remove Slow and return the Character to battle.
In addition to using Seize, the Tentacles can use Entwine to Slow and then Seize multiple Characters on the same side of the battle, and can cast both Poison and Bio. They can also counterattack with basic attacks, presuming they don't currently have a Character Seized.
You have a lot of options on how to fight the Tentacles. You can pound them all at once, potentially allowing one to absorb your attacks, or you can focus on their weaknesses or even Status vulnerabilities, taking them out one at a time. This is an annoying battle but not actually that dangerous (which is good, since it's been a long time since you had the chance to save). Edgar joins permanently once the battle is won.
The Crimson Robbers cleaned out the chests in the next room, but they missed the Soul Sabre hidden on the central statue. You'll have to walk back to Basement 1 facing battles all the way, but once you arrive Figaro Castle can finally surface near South Figaro. You can now have it travel to the Kohlingen Area as well. Looks like that's your next destination.
Before you leave, make sure to explore Figaro Castle. As in the World of Balance, you will get a shop discount if Edgar is your lead character. The Debilitator is now for sale, and you should pick one up if you haven't obtained one earlier via Steal or the like.