This walkthrough will explain only the basics of the underground as well as how to get the major weapons and armor in the level. There are many chests along the way that contain useful items, but this walkthrough will not describe each one.
Passage in Lunar Hideout
Go through the Lunar Path once again, following it the as before, continuing until you reach the Lunar Lair. This time, go behind the platform where FuSoYa was, to the door in the back. In this crystal room, there is a tile in the center. Stand on the tile and you will be transported to the Lunar Subterranean.
When you reach the underground, go immediately to the left and through a hidden path in the wall. On the otherside is a staircase. Go down these stairs. Continue forward on the path, and you will go down 3 sets of staircases, eventually reaching the podium where the Murasame sword is resting. You will have to fight the Pale Dim to get this sword. He has basic attacks, using the Slow spell occasionally. He counters summon magic with earthquakes, so be sure to cast Float to protect the party. When you defeat the enemy, you can equip Edge with this powerful sword. Return to the entrance of the underground.
Head down from the entrance, and go through the door. In the next room, follow the hidden path in the wall to the right, collecting the chests along the way if you like. Continue along the path, and you will eventually reach another door, continue through this door. In the next room, head down from where you enter, and take the first door you reach.
This next room is large, with several levels. From the entrance, head to the right taking the first staircase. On the next level, go all the way to the right and down the staircase. Finally, go to the left and into the first door you reach. In this room, head all the way to the left, and into the only door you see. Finally, go toward the southeast of this room, to go on to the next section.
Continuing to the Core
In the next room, go down the staircase, and into the next room, where you will head to the right and through the invisible paths in the wall, finally going through the door you see at the end of the paths. In the next room you will reach the next door you must pass through immediately to your left. Now head to the staircase immediately to your right when you exit the room.
In the next room you reach, you will find two bridges. Go down the one on the left, and cross an invisible bridge all the way on the left. Once across, go down the staircase at the end of another invisible passage at the top left of the island you are on. In the next room, head to the right, until you reach a staircase. Continue on the subsequent stairs all the way until you reach a room with a save point. Save in this room, and prepare to fight a boss.
Wyvern begins the battle with a meganuke attack that often kills some weaker characters, and then casts Wall on itself. Heal up before attacking in earnest. Never use summon spells on Wyvern, as he counters with more meganuke attacks. Instead, have Rydia cast Quake, since that bypasses Wyvern's Wall. As long as you don't trigger additional meganuke attacks, Wyvern is simple.
Once you defeat this boss, you can have Cecil equip the Crystal sword. Go backwards to the room with the invisible bridge, and the two divergent bridges.
Towards the Core
This time take the bridge on the right, and through the door around the path. Go through the door on the right in the next room. Finally you will come upon a save point in the first door you reach. Use this point because it is very important to be healed for the remainder of the game.
Leaving the save point, go into the next room on the right, and you will find the White Lance. Plague is difficult to defeat, as it places a 10 second instant death countdown on all characters. You have to defeat it before your time runs out. Since Plague is a flying enemy, Edge's boomerang weapons, Rosa's arrows, and Kain's spears all do extra damage.
Alternatively, you can exploit the AI. Any time Plague notices a character without the countdown timer, Plague recasts the countdown, but this resets everybody's countdown to 10. Therefore, you can kill and revive a fragile character like Rydia over and over to force Plague to repeatedly refresh everybody's countdown timer.
For winning, you get Kain's most powerful Spear.
The next room to your right contains two chests. Before you are able to open them, an enemy will attack you. These two dragons are not too difficult to defeat. If you use magic on them, they will remedy themselves, but Rydia's Bahamut is pretty effective, as it is far stronger than the remedy. You can't use magic on them because they cast Wall. Otherwise, simply use the strongest attacks possible. Finally, once you have defeated these enemies you are ready to move on to the final stage of the game in the Lunar Core.