There's not much to say about this level. You can just walk straight through it, unless you're aiming to get all the Secret Bonus Points, or you just feel like a bit of practice.
Begin by destroying the soldier ahead, and then further on, you'll find a hovering platform. Pull it directly down by grabbing the Hangman from underneath, and then grab it again to pull yourself up. After you get up onto the cliff, go right until you see another Hangman above you, which will take you to a ledge with a red soldier who fires cannon balls out of his face. When he shows his face, hit it to destroy him (or hit the ball if it comes out). Then, after him you'll find an enormous ball. Knock it off the edge to destroy the watch tower below, and keep going right. Destroy the sword soldier by pushing him down the hole on the right (or stand in front of him so he'll expose himself to attack) - if you need energy, you can jump over the hole and through the wall on the other side to find a jellybean. Above where the soldier was, there should be another ledge, so make your way up and up until you are next to another huge ball (you can get an extra life by knocking this ball onto a ledge slightly lower down, and using it to reach a higher platform further to the left; destroy the sword soldier, and use your head to reach the extra life floating over the edge). Then jump onto the cliff to your right and grab the upcoming Hangman from the left, as this is going to release a huge ball which will begin rolling down the hill. Follow the ball (but don't walk into it) until it falls down a hole, blocking the way for any more soldiers to climb out.
Next, choose either the Slammer (i.e. Hammer) or Super Head from Headcase, and make your way through the tunnel using the Hangmen (?) which come in and out of the walls. The Super Head will allow you to jump up onto ledges and shoot further so you don't have to wait as long for the Hangmen to come out. And the Slammer Head will cause more damage to Catherine Derigueur, who you will be fighting next. But first, you have to knock the cage into the hole so you can fight her. After you've done that, she'll start hopping towards you, so start hitting her. Before she corners you, run under her during one of her jumps, and when she arrives at the left side of the screen, she'll open her eyes and begin trying to suck you in, so just keep walking away and you'll avoid her. Then, she'll start hopping to the right side of the screen, and so, again, sneak under her, and continue hitting her. If she manages to get to the other end, she'll start pushing you away. Then, the whole sequence will begin again. When she's beaten, she'll start smoking and then fall apart. Watch out now as the two prisoners in the cage, Old McGee and Mule McGee, will jump out. Destroy them both to get two Secret Bonus Points.
Now, you have two different routes you can take. Personally, I never choose the mini maze, and it's the easier of the two, so I'll just go through the other route. Choose the Spike Head from Headcase, and use it to grab the wall further on. This may require some skill with grabbing in midair - try to imagine an elastic band - but once you've made it, you'll run into Snake Eyes, who will begin winding himself round the screen. If you destroy his scales first, then you won't be hurt by his body, so knock them all off by standing in one spot as he passes by. After that, you can just keep hitting his head, and when he stops, that means his going to shoot a large fireball, so get into a position to dodge. A good way of beating him is to get the Ticker Head and hit him while he's frozen (but make sure his head isn't in the ground or ceiling). When he's beaten (giving you a Secret Bonus Point), keep going right until you arrive at the end of the scene.
When, you walk in, Trouble Bruin will come along in his new machine, only to be crushed by the real boss, Mad Dog. Feel free to run past him, as his legs cannot hurt you. Go to his tail, and start hitting the end (you can start before Beau tells you to). He'll then jump in the air, so stay on the right side of the screen, because he'll come crashing down, and you don't want to be crushed by him. When he does come back, he'll drop one of four items. It could be a bomb, which explodes when it hits the ground; an egg, which releases three unicyclists who ride around the screen; a basketball, which bounces around the room for a few seconds; or Bino, who you can hit twice to give you another Secret Bonus Point. Anyway, while he's got an item run to the tail and continue hitting it. He'll then jump in the air again, and land on the right side, this time with no item. Now you just repeat the process again, as many times as needed, and he'll be beaten.
Certain heads can come in handy here. For example, use the Slammer Head to do twice as much damage to the tail, or use the Ticker Head to give yourself some extra time (while making sure that the tail is not out of reach).