Upon entering, you will see a big pit of lava, with fire spewing up. Don the Samurai Armor, and walk past the guards safely. You will now walk dow a corridor with jail cells on both sides. at the end of the corridor you can see the cell Rioichi is in, which is a small cage that is surrounded by a giant pit.
On your left, you will see a small room. there is a crallspace, and then an area with a large table the guards are eating on. As you keep moving, you will begin to walk on a rounded, wooden bridge. You will now go through a large open gate, and there will be a long, twisting path. Along the path, dragon statues will blow fire at people passing by, axes on chains will slice along the path, and wooden spikes underneath the path. A rock spire splits this path from another path that looks the same way. At the end of the second path, there's a wooden floored area.
A wooden bridge comes next, which is split in the middle. Another short corridor comes next, and a wooden area following along the wall follows after. Along the wooden area are more stone dragons that blow fire. Afterwards is a rope that Sly can ride downwards with his cane to a small cliff-like area. Next is a pole that Sly can climb, that comes to another cliff area. Sly sneaks along the edge of the cliff, and next comes a rope which Sly can climb.
Another wooden platform is where Sly will climb. Now comes another bridge split in the middle, and a lava/fire fountain like at the beginning. A closed gate is on the other side of the fountain, which will only be opened by a key that you should pickpocket from a guard.
Finally, a path would bring Sly to Rioichi's cage, except for there is a pressure plate that makes that path fall through. Two giant fireball-breathing dragon statues rise from the pit, and you should deflect them with the Samurai Costume. as soon as you destroy the two statues, a way to advance will rise from the pit, and two more statues will rise again. This will continue multiple times, and it will be mission complete.