Begin by hitting the the orange ball to change the landscape. doing this will cause tumblees to roll about, so don't get hit by them. After hitting the orb, jump onto the second tumblee, destroy the structure blocking your way, and hit the second orb (which is now blue). You'll quickly have to jump off the tumblee and to the left, as it will begin rolling to the right. When it's finished, jump on it again, and hit the next orb to raise you high enough to reach the platform in front. To drop through the floor where the first Hangman is, you can either jump and grab down at the Hangman, or simply duck and then press jump. After that, make your way to the platform with Headdy's face on it, and grab the Hangman to flip the stage.
Don't worry about the falling debris; just make your way to the right, but walk slowly along the orange platform, otherwise you'll miss the Headcase which appears when you reach the bottom of the slope coming up. Grab the Slammer Head, and go as far as you can to the right. Now Mons Meg will appear, so just keep hitting her face. Avoid her left side, as this is where she slams her fist, and when her eyes turn into targets, she will try to put a target on you, so run from it when it stops moving, because bullets are about to be fired. But if you keep hitting her (with the Slammer Head), then she won't have time to fire, and will switch back to her fist. The Slammer Head should bring on her demise twice as quickly. Further on, you will come across a series of blocks that you have to knock out. Grabbing another Slammer Head will speed things up. And if you grab the Vacuum Head each time you run into a Headcase, then you'll be able to suck up nearby objects that are otherwise out of reach. After all that, you'll approach another platform with Headdy's face on it, so grab the Hangman above to flip the stage back to normal.
Next up, you'll find the Happy Campers, who like to jump out of a hole in the ground. When you are in line with one, knock it onto the pole on the right. Do this four times to create a reachable ledge and then go up onto the ledge with the Headcase on it. From there go to the left and knock the remaining Happy Campers onto the pole to the left. Jumping onto this newly formed ledge will take you to a 1-up. Continue to the right after grabbing the Empty Head, and you'll meet the Super Tank Machine. He'll fire a cannon ball straight forward, so hit it diagonally up, so that it gets stuck on the spikes above the driver. If your aim is true, it will fall on him and destroy the machine, but if it misses, then you'll have to wait as he continues to fire two types of balls. The alternative type of cannon ball that is fired falls out and bounces on the ground, so just bash it away. Anyway, After he is beaten, proceed to the funny-looking with eyes, and bash it till it is no longer covering the drain, so a fountain of water will appear to bring you up to the upper platform. Again, you'll need to flip the stage, so find the Hangman and grab it.
Ahead, there's another Headcase, so grab the Vacuum Head, and suck in the items out of reach. Then cancel the Vacuum Head, grab the Slammer Head, and start hitting the large pendulum (be careful only to hit it when it moves away, because otherwise it will lose momentum). Once it goes as high as it can to the other side, jump on it when it comes back so you'll swing to the other side. For the last part of the level, you'll be passing the Funky Jeep Men, who shoot from their front and can only be destroyed by hitting in the back. The blue/orange orbs change the direction of the conveyor belt, making them change direction, too, to avoid falling off. I usually keep the blue/orange so I can hit them from the left, since that's the direction I'm coming from.
First, walk up to the Headcase and grab the Slammer Head. Then go to the left of the blue ball and hit it. Keep hitting it (when it swings away from you) until you can jump onto the platform on the opposite end to the ball. This will bring you up to a higher platform on the left with a crocodile statue. Hit it, and a ladder will shoot out. Climb the ladder and make your way to the right on the light-bulbs, past a slightly lower platform, onto an even lower platform, where you'll now see a series of conveyor belts with platforms. Jump onto these platforms, being careful not to run into one of the Wise Women or onto a platform which is about to tip over. Make your way upwards, and past the next animal-statue-with-ladder-inside, to reach another platform with a Headcase on it. Grab the Slammer Head, jump down and bash the blue block to get through the pillar, and continue to the right, past the blue ball, past the next animal-statue-with-ladder-inside, past the Hangman, and up to the next blue block on the right. Hit it, go down the tunnel, and grab the 1-up at the end. Then go back, make your way back to the Headcase by the second blue ball, and grab another Slammer Head. Bash the blue ball until the platform comes along, and use it to reach the next vertical conveyor belt, where you'll be able to destroy two more blue hammer blocks to open the way to the next scene.
Be careful not to walk into the spinner without destroying the soldier first, and then you can pass it by standing on it and hitting downwards. Pass the next spinner and decide whether to go up or to the right (personally I don't go up, but you can if you want to).
If you go right, grab the Hangman, and then grab a War Head from the Headcase. This will allow you to travel safely to the right while the enemies on the ceiling and floor explode in your path. Be careful not to hit the spinner downwards, otherwise you'll be sent down with it and might be trapped under it. When you reach the wall, make your way up.
If you want to go up instead, then get on to the spinner by jumping and hitting upwards. Do the same with the next, and then proceed to the right, to a fan. Hit the fan to stop it blowing the spinner, giving you the chance to climb up it and over (if you want, you can destroy the fans by hitting them every time they start up again). You'll have to pass another fan, and before you leave the level, go down and grab the 500s below.
Only one thing I can mention here, and you don't have to get it, but if you wait for a few seconds, then Bino will appear to clean the windows. Repeatedly hitting him will eventually reward you with a Secret Bonus Point. After that make your way to the right and Beau will tell you that Heather's beaten you to it (whether there was ever a Keymaster, we'll probably never know). And there you go - the easiest boss scene in the entire game.