The next time you take Figaro Castle back to Figaro, it will hit something. You should explore whatever it is.
Find the Ancient Castle
Go to Figaro Castle, then talk to the old man to have him take the castle back to Figaro. When you hit something, choose to stop and explore. Then go up the stairs to the right, and in the next room, go down the stairs to the right. You should be in the jail. Go into the far-right cell and go through the door in the back.
208. Goblin/Devil
209. Figaliz/Figaro Lizard
Go southeast and go past the stairs, then go south and open the chest that you see there. Then go through the southeast door, and if you wish, you can open the chest there to fight Master Pug/Master Tonberry. You will get Graedus/Gladius if you win.
Master Pug/Master Tonberry
Master Pug/Master Tonberry has a special move called Step Mine/Traveler that causes damage based on the number of steps that the target character has taken throughout the game.
Master Pug/Master Tonberry will use the WallChange/Barrier Change move to change which element it is weak to. After doing this, it will cast spells that are the opposite of its barrier. In other words, if it casts Fire spells, use Ice spells against it, and so on.
Master Pug/Master Tonberry slowly steps closer to your party, and after taking seven steps, it uses Cleaver/Knife to deal 14 attacks worth of damage to one person, surely killing him or her.
Since Master Pug is vulnerable to Sleep, you can use Sleep and then attack with non-elemental magic, giving your party some time to attack without waking it up.
After Master Pug/Master Tonberry
Whether you battled Master Pug/Master Tonberry or not, go west through the wall, then go north and through the door. From there, go west, then open the chest south of you, then go south through the door.
Follow the straightforward path to find a chest, then go south, then west through the wall. From there, go north, then go west through the wall to reach the next area. Go south past the stairs, and keep going south to find a chest. Then go northwest to find another chest. Then go north and east, and go down the stairs that you ignored earlier.
Save at the save point, then go up the stairs on the left.
Ancient Castle
211. Boxed Set/Lunatys
Go north, and there will be a cutscene. Then go north until you find the Odin statue. Check on it to get the Odin Esper.
Fight the Blue Dragon and Change Odin to Raiden
After getting the Odin Esper, you can optionally use a secret passage to fight the Blue Dragon, and you can also turn the Odin Esper into Raiden. This change is permanent. Some players choose to wait until later to transform Odin into Raiden, because (at least in the SNES version) Odin is the only Esper that increases speed on level up, while Raiden increases strength on level up. Odin teaches Meteor, while Raiden teaches Quick.
If you do want to fight the Blue Dragon and/or turn Odin into Raiden, then walk up to the throne on the right, then walk down five steps and press A. A passage will open. Go east and enter the small passage in the east wall.
You can read the queen's diary from the bookshelf. Then go down the stairs.
In this room, the Blue Dragon is flying around.
Go north from the dragon and check on the statue above to change Odin into Raiden.
After Castle Basement
Go back up to the throne room using the stairs in the southwest corner of the room with the Blue Dragon and the statue of the Queen. In the throne room, use the door that is second from the right. Open the two chests, then exit the room.
Go south until you are outside, then go left and enter either of the two doors. If you open the chest, you will fight KatanaSoul/KatnSoul/Samurai Soul. If you win, you get the relic Offering/Master's Scroll, which allows you to attack four times in one turn.
KatanaSoul/KatnSoul/Samurai Soul
This enemy is weak to Poison. It throws Edges/Scrolls, and uses the special move Gale Cut. If it is hit three times with magic, it counters by throwing a katana, then using GP Rain/Gil Toss. If hit with six normal attacks, it uses the move SlayerEdge/Assassin Blade, which kills its target. Eventually, the enemy will cast Blink, Rflect/Reflect, and Haste on itself.
If you Muddle/Confuse this enemy, there is a chance that it will use SlayerEdge/Assassin Blade on itself, killing itself.
After the Monster-in-a-box
Exit the room of the Monster-in-a-box, then go east past the castle entrance. Go through the small door there and open the chest. Then you can go south to return to the cave. Go up the east staircase, then go northeast. From there, go south, then east through the wall, then up the stairs on the right, then go north and go through the door. Go east through the wall and then go through the south door. Go east through the wall, then north through the door. Go northwest and through the door, and you will be back in the Figaro Castle jail. Go up the stairs, then go west down the stairs, and ask the old man to Continue Journey. Afterward, you will need to ask the old man to go to Kohlingen and tell him to continue the journey after you stop again. Then you will be able to return to the Airship.