Well, it's time to find Dr. Wily and put an end to his schemes. When you appear on the ledge, climb up the ladder to your left, then the next ladder to the right from there. Climb that ladder and from the top of it, hop left along the ledges to the next ladder. Along the way, you'll have to take out two of the hardhat enemies. Defeat them and climb that ladder into the next room.
There are four of the hardhat enemies in this room. You'll have to take them out as you go, but know that they're of a tougher variety than normal. Some of them will push up their hats, then whirl like tops as they fire shots in your direction. Others will succumb to a simple shot. Try to take the least damage possible as you proceed through here, of course, but know that you may take a fair amount of damage just due to the cramped quarters. When you've cleared the area, climb the ladder at the upper left corner of the screen, to the next hallway.
From where you appear here, head toward the right. This area is filled with more of the hardhat enemies (getting an idea for the sort of boss you'll face at the end of the stage yet?), and you'll again want to do your best to avoid those that you can while dispatching of others that stand in your way. Partway through, you can leap up to an upper ledge and slide through to collect a large energy capsule, which you likely need. When you reach the pit near the wall, drop down to the room below.
You're now at the stage's checkpoint. From there, drop down the pit to the left and you're underwater and mostly surrounded by spikes. Make sure that as you fall, you're pressing against the wall on your right. Otherwise, you'll land on a set of spikes that line the left wall below. From there, head toward the right and shoot the hardhat enemies as you go. A short distance to the right, you'll come to a ledge that looks over a narrow corridor ahead, where both the ceiling and the floor are lined with spikes.
It's not really possible to make this jump and survive without nerves of steel, so go ahead and switch to the Rush Marine and glide through the area in your handy submarine. You only need to use it for the short little stretch, shooting a hardhat enemy along the way. Then the rest of the trek can be made in your normal form.
When you climb up the ladder into the next screen, make sure you ascend to the very top of the ladder, or else the enemy patrolling at ground level will slam into you and cause some pretty serious damage to what is likely a dwindling life meter.
From the top of that ladder, use disappearing/reappearing blocks to cross. The first block will appear just in front of you. Hop over to it, then immediately jump straight up to land on the next block. The rest of the jumps require no explanation, until you make it across to the ladder.
In the next room, the floor is lined with spikes. These blocks appear in an order that is rather difficult to anticipate. Watch until you have a sense for the pattern. Watch for the first two blocks that appear simultaneously, and note the location of the left-most of those two. Now note where the one appears just to its upper right, a few blocks later. When you are familiar with the pattern, you can jump to that first block, then jump to the next one just before the first one vanishes. From there, it's a simple jump to the next block to the right, then the next from there. Once you land on that block, jump directly up to land on the last of the blocks. From there, jump to the gray beam at the top of the room. Walk left to the ladder, then climb it into the next room.
In this next hallway, there's a hardhat enemy sitting in the middle level. Move right past it, or destroy it if you want the special weapon refill. Keep moving and you'll see that there are more of the hardhat enemies. Many of these rest within tanks of water. Jump up to shoot those, and grab the energy tank. From there, move right and you'll find the gate leading to the boss battle.
NEXT: Stage Two