This rain-drenched stage you should be tackled first. It's a great place to get used to your new abilities, and the robot encounter at the end should be a breeze for you.
From the start, head right along the brick towers. You'll be working against driving rain, so note that when you jump and it's blowing against you, Mega Man's jumps will not take him quite as far as normal. Before death-defying jumps become a concern, though, you'll want to focus on the birds and their young that are out in the storm. Large birds swoop down and send their young flying toward you. If you have your arm cannon powered up, one good shot will take out the flying flocks of birds. It's likely that one will sneak under your shot, though, so be ready to fire another quick shot or to slide.
Another hazard in this area is the enemies that glide down from the top of the screen using their umbrellas as parachutes. Again, a charged mega buster shot takes them out right away, but you have the birds to consider, too.
When you're past a few of these enemies, you'll come to the series of jumps over gray-colored scaffolding. Here, more of the birds and umbrella robots will attack, but not with the same frequency. Watch the direction of the rain in the background as you continue toward the right. It will let you know how much resistance to expect from the elements. Regardless, though, you should always jump from just near the right edge of the platform, and you should press hard to the right in order to just barely land on the next ledge.
Past that series of ledges, there are more birds and parachuting robots before a pit that will drop into an empty room below. When you land, power up your mega buster before dropping down the pit along the screen's left side.
When you land, you'll be in a slow, shallow rivulet of water that is pushing you toward the right. Move slowly right and you'll soon come in contact with this area's two opponents. One opponent takes the form of bulbous robots encased by gel. They crawl along the ceiling and will drop toward the water as you near. Two normal arm cannon shots will take them out quickly, so you shouldn't worry much about them so long as none of them catch you in the midst of trying to leap over a pit. Just watch the ceiling whenever you're making jumps.
The other hazard is similarly simple to avoid. Robotic rats inhabit the area, and they move rather quickly. Again, a few rapid shots from your arm cannon will remove any threat. Other than those two hazards, this passage is actually pretty simple. You can tell where ledges are (even when they're not fully in sight) just by watching where water drops in small waterfalls. Land between each set of tiny waterfalls and you'll be fine.
Make your way to the far right of this area and you'll drop into another empty room. Again, you should power up your mega buster before dropping down to the next room.
Here, you'll be attacked by what looks like a giant snail. Its only vulnerable spot is its eyeballs. The snail will attack in two ways. First, it will heave bombs your way in an arc. You can leap these, or slide under them. When it tires of tossing bombs, it will send its eyes outward in a diagonal arc that is much more difficult to avoid than the explosives. You need to be ready for either attack, as there's no solid way to predict which will come. Just keep dodging and firing and you'll disable this guy in no time.
When that fellow is gone, head along to the right. There's more shallow water, which drops down as a pit comes. Slide down the hole along with the water, and hold left as you do so. In the next screen, you'll land on some scaffolding. Below, one of the rat-like robots will be hopping about the water. Drop down the pit to his left while keeping your mega buster charged.
You now are in another room with a giant snail. The difference here is that you don't have quite the room to work with, due to flowing water that is trying to push you off either side of a ledge. Standing directly under the rushing water from above will also prevent you from jumping well. Stick around to either side, dodging snail attacks and countering with your own as possible. When the snail is done for, continue right into the next screen.
You're now at the edge of a wide pool of water, with gray platforms overhead. You'll need to use those to hop along to the right, while avoiding fish-shaped robots that leap from beneath the water to try to knock you to your death on the spikes that line most of the area.
As you walk right, just keep hopping slowly, from one ledge to the next. Mega buster shots will take care of any fish that jump from the soup. The platforms can be difficult to reach if you're worried about the fish, so either destroy them or let them pass out of the way before making each leap, particularly the one that forces you to land between two ledges. Halfway through, you'll find solid ground for a moment. While there, shoot any fish in the way, then hop out of the water and take the last few leaps to reach the gate leading to the area's robot master.
NEXT: Bright Man