I was doing some tests and I've found out that 6 of the 8 stages can be beaten without pressing the A button.
Toad Man: Rush Coil is your friend, and there are no awkward obstacles or anything, but the snail mini-bosses are difficult to deal with with Rush Coil. Toad Man is also the easiest stage without any extra weapons, plus you get Rush Marine.
Dust Man: Another stage that can be beaten moderately easy (considering the challenge). There is one difficult part; near the fourth section of shootable blocks, you have to use Rush Coil to hit one of the blocks in the third (I think it's the third one) row from the top as the ceiling is coming down to create a sideways L shaped hole, so when you go running across, you have a safety spot. There's no other way to do that section. Also, Dust Man is somewhat easier if you grab an Energy Tank from Fliptop. Rain Flush is also handy to have when you're going across the rooms with all those flying red baddies.
Drill Man: After the screens with the spikes comes a staircase that looks impossible to reach the ladder since Rush doesn't fit unless you use it from the step below. But, if you have a baddie hit you when you're on the top step, you can have Rush warp to you and allow you to climb the ladder. The next hardest part is the final jump. You have to use Rush and get hit by the stuff that drops out of those holes (I call them rocks), knocking you off the edge where Rush warps and boosts you. Drill Man is also hard to beat without Energy Tanks, but there's one midway in the level.
Dive Man: There's one place where you have to slide to get to, but Rush Marine can get you past there. The next tricky part is when you're on the ladder and there's a gap, you have to use Rush Jet from the ladder at the appropriate height, jump on him, pull back and lift up. Rush Marine takes care of the water areas. Wire is also necessary for a later level. Dive Man is tough without being able to jump, but Dust hits him for 3 damage, and you can get an Energy Tank.
Skull Man: This one is fairly easy, but you need to do multiple bosses first due to one of the early rooms. The room with the first bone throwing enemy has no room for Rush and you need to use Wire to get up from there. The rest is easy, especially with Dust Man's weapon.
Pharaoh Man: This is tricky. Rush Jet doesn't work on quicksand, so you have to walk up to the edge of the starting platform, use it behind you, let the green (scorpion?) monster hit you so Jet will warp. Then when it's touching you, you have to go down into the quicksand with it while holding down. Eventually it'll catch up to you and you can hover across. It's also possible to get Balloon here. The stage is pretty rough, but with Wire, Balloon, Rush Coil and Rush Jet, your sources are plentiful.
Ring Man: So close. I actually am able to do this with just Rain Flush and Rush Coil, but it's extremely difficult to say the least. First off you have four mini-bosses (although Rain Flush helps), and the platforms that shrink towards you (the brown ones) require a tricky jump. To get across them, you need to use Rush at the edge of the beginning of one so you get height before it starts, you run as far as possible, summon Rush Coil again, fall, and jump back up before it closes. You have to do this a few times. Of course Rush Jet can work too. The problem is that at the very end you need to slide.
Bright Man: This stage cuts you off early. You don't get very far before you come across a point where you have to slide. Otherwise, it's not that bad.
I did a test-TAS of a few levels and I think even if I prettied it up it's not that great to watch, but in the case that anyone wants to challenge themselves, well there you go.
I'm going to move on to another game now and tear something new up. I think I've dug as deep as I can with Mega Man 4, but I would love to see any new glitches players find.[/b]