Wily escapes in his ship, and the map shows a second boss marker underground. Mega Man appears in the middle of falling down a long shaft.
The first thing you'll notice after landing is the lack of music, and the only sound here is the dripping of whatever red stuff is leaking from the ceiling, which can kill Mega Man in three hits. This section is doing a great job setting up the reveal here, as the creepy and out of place setting would almost make you believe that Wily is actually...
Alien Wily floats around the room in a figure-eight pattern, shooting at you now and then. The only thing that can damage him is Bubble Lead, and it deals one damage per hit, so if you walked in with a full bar you'll need to hit with half of them. While that's not difficult to do, it's very easy to die here if you're not taking it carefully, since you'll need to get close and those shots hurt. This sets the tradition of Wily being weak to the most difficult weapon to hit with, but the fact that you can't hurt him with the Buster causes the same problems we already went over with BooBeam.
Aside from the weapon requirement, the setup and reveal for Alien Wily is great, and the fact that his pattern is so simple is a reasonable decision here, as his whole purpose seems to be an attempt to scare the player into making mistakes rather than being truly difficult. I'd argue that the first two forms are actually worse than the first game's though.
Overall though, Mega Man 2 swung pretty heavily between being awesome and being unnecessarily frustrating, though there's much more of the awesome.
I can't think of much to add for this one since I covered it more thoroughly than the first, so the one last thing I want to say about it before moving to on to Mega Man 3 is that nearly every time the game gave the player too much grief, it did so with style. Stuff like Heat Man's bridge and BooBeam were the sort of things that got talked about around school, and instead of just being annoying like Foot Holders, they had a flair to them that tends to stick with you. People may have torn their hair out over Quick Man's lasers, but you don't forget that sound. If the dragon kills you when it warps in, you're not likely to bitch about it much because holy crap a robot dragon just warped onto the screen!