No matter what order you tackle the four Robot Masters in, you'll be tossed into the Robot Museum after defeating them all. Enjoy the cameos in the background on your way to the boss door. Dr. Wily will steal Guts Man, one of your foes from way back in the first Mega Man game, and you'll have to fight Mash.
Mash mostly just hops around. Its weak point is its head, but you'll need to knock it clean off its shoulders to damage it. When its head stops spinning, shoot it right in its ugly face with a fully charged shot to blow its head off. It will bounce around and land on the floor, so shoot it some more with another charged shot or two or three. Don't hit the body, it will just absorb your shots. Regular shots will fly right over the head of its sitting on the floor, so use shots that are at least charged a little bit.
Mash does have two weaknesses. Hit his head with the Thunder Bolt to knock it off, and then hit it with Danger Wrap to do a good bit of damage to it.
That's all there is to this level. Four more Robot Masters will appear on the Stage Select screen, but we have some backtracking to do first.
Head back to Cloud Man's stage to get the letter U. Then head to Junk Man's stage to get the letter S. This will earn you the Super Adaptor, which will let you equip Rush as a suit of armour. This will allow you to press the jump button while airborne to fly diagonally upwards a little ways, and it will replace your charged shot with a shorter ranged (but more powerful) flying punch. Keep in mind that you can exit stages you've already cleared from the pause menu, using the Exit item we collected in Freeze Man's stage.
NEXT: Turbo Man