Return to the central platform and hop onto the stone ball. Roll around the west side of the central platform. Continue to the northbound bridge and roll into the switch (the protrusion) to cause one platform to rise a bit. Also be sure to check the northwestern isle - it has some Rupee-yielding dig areas and a random-treasure treasure chest.
Afterwards, go to the east-central wall of the room. Along this area, you should be able to see a crack in the wall. Throw two Bombs at it to create a hole and a new path. Follow the path for a bit - along the way, be sure to stop at the small room for a Bomb refill.
Further along, you’ll be blocked by a large platform. Turn around and look around for a crack in the wall - throw two Bombs at it to create a new path and a fight with a Fire Keese swarm. Continue along the new path to get around the middle platform. Continue forward to the gate. This one has a mechanism similar to the drawbridge from early in the dungeon. Use the Beetle to slice the rope on this side of the gate, then go through the tunnel on your left to reach the opposite side and the other rope.
After the gate rises, go forward to the ledge. Go through the passage, defeating a few Bokoblins along the way, to reach the Bird Statue. Save and return to the stone sphere. Go further ahead, and continue whenever the lava ceases to spurt from the walls. Afterwards, carefully traverse the narrow path to reach the main portion of the room. Bump into the switch on the platform from earlier to finish the bridge properly. Get onto the bridge, use it, and go through the door.
In here, go across the gap to find a steep incline. Hug the left wall as you dash up, going into the alcove when possible. Let your stamina recover and then go to the hill’s peak. Here, go into the nearby tunnel. On the other side, dig around to reveal an air vent. Use it to reach a ledge. Follow this path to find a nice little balcony overlooking the second incline. Withdraw a Bomb and aim above the dirt patch or so - if you’re lucky, you should destroy the rock barricade partway up the incline.
Go back through the tunnel and dash up the incline. Go into the alcove when possible and restore your stamina, then make a mad dash for the top of the incline.
At the top, use the nearby Bird Statue, then go up the nearby winding path. At the top, you’ll find a chest, in which you’ll find the Dragon Sculpture. As you proceed to go back down, a boulder will be launched down the incline after you! If this thing hits you, it is an instant Game Over). Make a mad dash downhill, grabbing Stamina Fruits along the way. If you succeed, you’ll stop the lava flow. Use the Bird Statue again, then proceed to insert the Dragon Sculpture into the door.