From the start of this stage, hop up two levels so that you're at the third chute from the ground level. Slide along the path and be prepared to shoot out the other end and press to the right so that you land on a ledge over a pit of spikes.
Jump from that ledge to the next, and from there to the top of a ladder. Descend the ladder into the next room. There are more ledges here over spikes, and flying enemies will try and attack you. Cross over the ledges to the left and drop into that pit, then from there land on a ledge in the next room, just to the right of where you would normally fall.
From the new block you land on, position some Balloon platforms so that you can ride them up to an energy tank. Now that you've done that, drop down the right of the two pits along the floor in this room.
You're now moving along a raised ledge. As you move right, shoot the worms that will drop from the ceiling. When you reach the end, slide down to the platform below. There's a robot patrolling the ledge ahead, so shoot it with some pharaoh shots and get it out of your way. With that done, you can use some more Balloon platforms to cross over the pit to the ladder to your upper right.
Once you've climbed the ladder, you're in a room where Fliptop will make an appearance. Collect the goody he leaves, then climb up and exit the room using the ladder to the upper right.
In this new room, you'll see ledges that will allow you to jump up near the top, where a worm should have dropped by now. Shoot it, and work down through the ledges, and then back up to the ladder along the top of the screen. Climb it and you're in a long chamber with several platforms suspended in the area. Just walk along the lowest level, charging your mega buster and firing as necessary to blast the mummies that will appear from the background to toss their heads your way (you should remember them from Pharaoh Man's stage).
There's a ladder at the opposite end of that passage, and it leads up to a new room with three bats. Take out the bats, then turn your attention to the two ladders in the room. You should take the upper right ladder, so that you can climb up through the next room, shoot the skull-shaped enemies, and slide through a gap to grab a ladder that hangs over a pit of spikes.
Climb the ladder and you'll find two of the rolling enemies in the next room. Shoot the first one rapidly before it turns itself invulnerable, then hop over the small gap between the ladder's top and the platform. Walk over to the right, then jump up to the next ledge. Face left and shoot the second enemy, then slide under and walk to the next ladder. Climb that and you're in the next room.
You now can come to the top of the ladder and look to the right to see another of the red, towering enemies from the early stages in the game. Just keep jumping to avoid its shots, and fire your own in return. When the machine is done, you're ready to hop over the blocks to cross the spike-lined area ahead. Get to the other side and there's yet another pit of spikes. More blocks hang in the air over these, and you can cross over those to get within range of the robot. Defeat it with more shots, then jump to the next ledge it occupied.
From there, you can go ahead and keep moving right, then pass through a gate to the boss of this particular area.
NEXT: Stage Three