Walk to the right to find the first boss of this stage.
Boss: Fire Dragon
The only thing that can damage this boss is your Ice special so switch to it if you haven't already. It doesn't attack though. It randomly appears in a spot, runs towards you, and then jumps into the fire in the background. Wait until it materializes completely, hit it if you're far enough away, jump over it, and then try to hit it again when it's bouncing around the side of the screen. Keep doing this until you kill it. It takes a while so I hope you're patient.
Head to the right and you'll come across a tunnel lined with spikes and several Robot Crabs inside. Kill the Robot Crab that you can see, switch to your Upside Down special, and then continue through the tunnel. When you reach the other two Robot Crabs, hit them as fast as possible, and then walk to the right until you reach safety again. By the time you reach the far end, you will be almost be out of time. Further to the right, you'll see many Yellow Robots. You can kill them with one fireball each but they will probably swarm you and possibly causing some damage.
Soon after that, the floor will start slowly rising upwards. Walk to the far right, killing any Yellow Robots that appear, and stay there until you clear the spikes. Walk back to the left until you pass the spikes again. By now, you should see the outline of the huge robot in the background through the gaps in the wall. You'll do two more repetitions, first to the right and then back to the left until you reach the head of the robot in the background. Really try to conserve your health up to this point. You'll need it. But about the robot head. Guess which boss you'll be fighting against next...
Boss: Robot Head
The head will disconnect from the robot's body and start flying around. Notice the drill at the bottom of its head? You need to avoid that. The head will make that harder by occasionally dropping it into the ground to try and hit you. You can tell when it's about to drop because it will stop moving for a few seconds. When it drops, you can damage the head. Keep doing this until it's destroyed.
Continue to the right and you'll meet the final boss.
He'll talk for awhile and then make a dramatic fade in appearance. He'll then start to fly around and when you walk until him or just wait long enough, he'll shoot a stream of electricity out of each of his hands and occasionally a fireball downward from his mouth. The only way to damage him is to hit him in the mouth with one of your attacks. Stand under him to make him use his electricity attack and then walk along with him and wait for him to open his mouth. When he does, hit him in the mouth. I find that the explosion fireball is best because it allows some leeway and you won't have to stand directly under his mouth to damage him as you would with your other special attacks. Keep doing this over and over again and he'll eventually die.
The game is now finished.