Drop off the rope and quickly kill the punaguchi on the floating platform. Jump on this platform, then time your next jump so you land on the extending spike at the bottom. Once you jump onto this, quickly move right and then go down the rope. The next room is a small one, with two big bats in it, kill them and then use the rope to get to the next room. This is another small room with a floating platform in it, jump onto it and carefully kill the punaguchi before heading through the door.
The next room is a long corridor, where lots of mud men will keep appearing. Fight them off and keep going right until the scenery changes, then hit the single candle you see. This contains a crystal, collect it to make the Bone Dragon King appear. This creature bursts through the ceiling and floor of the corridor. What's different with this boss battle is that the screen is constantly scrolling to the right.
You can tell which hole the boss will emerge from next as it will shake about a second before it appears. Due to its length, the boss can appear out of more than one hole at the same time, so try and keep to the right of the screen to avoid being crushed. Touching the boss will result in a large amount of damage, but this is the only way it can hurt you, it doesn't have any other attacks. The only place you can hit the boss is on its head, so be ready to try and get a couple of attacks on it whenever it bursts out of a hole. Once defeated, the Bone Dragon King will explode into nothing.