Cave to the Sealed Gate
*Many of the enemies in this area fall into the undead category, so be sure to have plenty of healing items and spells on hand. Phoenix Downs and the Raise spell will act as insta-kills against tougher enemies.
To reach the Sealed Gate, you must first pass through a small Imperial base. The only building within is locked: there is literally nothing to do here right now, so move on.
The cave leading to the Sealed Gate is comprised of three levels. From the entrance, head east from the short stairs to grab an Assassin's Dagger before continuing to the next room. Go down the stairs on the left side of the screen and pick up the Kazekiri before using the stairs on the right to enter a chamber that is full of shifting bridges and lava.
The aforementioned bridges will shift positions once every thirty seconds or so. If a bridge changes while you're standing on it, you will fall and land back at the room’s entrance. With that being said, take a moment to stand and watch how and when the bridges will change. When you're ready to move, navigate to the rock platform near the middle of the area. Wait for the bridges to change again before going south, then west to claim the Heiji's Jitte relic from the lone treasure box.
Provided the bridge under you hasn't collapsed at this point, make your way back to the platform to the north, and cross to the solid ground to pick up an X-Potion from the chest. From there, follow the southern bridge and stay to the left as the platforms shift to reach the next area.
When you reach B3F, head to the east to pick up a Hi-Ether before backtracking to the room's entrance. From there, take the stairs down and follow the path through a small cave. On the other side, follow the southern path up a small slope and cross the bridge; about halfway over you will see a switch. Pull it, and the bridge will break, and you will hear "a distant sound." Go left and follow the path north until you reach a small island with a lone treasure chest. Take the Genji Glove from the chest and backtrack to where the bridge dropped you. Head east from the broken bridge and up the stairs, where two switches sit on either side of a rock wall. Flip the switch to the left to open a door in the empty space: inside will be a Save Point and a Tent. The switch on the right will lead to a random encounter with a Ninja. Luckily, he's not a threat; he'll lament not claiming some treasures beneath a grand stairway before he dies. Make your way across a bridge to the east, pulling the switch as you go; this will open a long stairway leading south. Don't go too far ahead yet, as these next treasures are very easy to miss.
As soon as you are off of the stairs, take one south followed by one step west and hit your action button to pick up an Invisibility Scroll. From there, take four steps east and two steps south to discover a Water Scroll. Now, take four steps west, followed by four steps south to pick up a Gold Needle. Go to the chest and take the Hi-Ether, then take three steps north to find 293 gil buried in the ground. Now that you have successfully looted the poor Ninja’s treasure, proceed through the small cave to the east and wiggle around a little bit until you come out on the other side. Open the nearby chest for an Elixir.
Head east, and you will notice two stepping switches. The first will open up a nearby stairwell that leads to a dead-end, and the second doesn't do anything immediately beneficial. The second switch is placed directly in front of a bridge and will break it apart. You can simply walk around it to reach the nearby treasure chest, which contains a seemingly useless switch. Make your way to another switch located in the southwestern area of this area and push it; a door will open nearby, leading to a room housing several treasures: two Magicite Shards, a Hi-Ether, and -- most importantly -- the Ultima Weapon.
Leave the room and head east; cross the bridges to the north, and press another switch to raise a platform to the right. Follow this new path, and head north to find a chest containing a Magicite Shard. Make your way to the southeastern door and follow the linear path to the Sealed Gate.
When you regain control you will be thrust into a quick battle (sans Terra) against Kefka. One good hit should end the fight and trigger some esper-related shenanigans. After everything goes down, you will find yourself back in the chamber that lead to the gate -- with one noticeable difference: a door leading back to the cave’s entrance will now be available. Use it to leave the cave, and then head back through the empty Imperial Base (there’s still nothing to do). The inactive party members will meet everyone at the exit, and the group will go back to the Blackjack.