Someone asked me about this boss in the comments on my D-Rex video so I decided to make a video for it. I hadn't played Mega Man X in quite a while so I was a bit rusty at first (accidentally doing regular wall jumps instead of dash wall jumping got me killed a fair bit...) but playing through the first two Sigma levels to reach Rangda Bangda got me back into the groove. Though it helped that this boss doesn't require especially fine control.
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Mega Man X - Rangda Bangda - No damage
Rangda Bangda beaten without taking damage using the X-buster. Its weakness is the Chameleon Sting.
Rangda Bangda is made up of three parts—two eyes and a nose—which will take turns attacking. While one is active the other two can neither take nor cause damage so don't worry about them. And, while there's only one life bar on screen, each section must be destroyed separately. Rangda Bangda's attacks themselves are not very powerful or hard to avoid but it's instant death if you get knocked onto the spikes in the center of the floor.
The eyes have three ways of attacking, which you'll be able to tell apart by their color when they open. Blue means that it will fly out in a straight line towards you, which is easily dodged. Green means it will shoot a single fireball directly at you, which is also easily avoided but doesn't allow much time to counter-attack. Red means it will shoot a spread of three fireballs at you and sometimes also fly towards you at the same time. There are a number of ways to dodge the blue and green attacks, depending on where you are in the room, but for red attacks you should always stay on the opposite side of the room so you'll be able to slip between the fireballs.
The hardest part of the fight comes when the nose attacks. It will close the walls in on either side of the room so that the only floor left is covered by the spikes, forcing you to cling to the wall. It will then move around in one of two patterns. To dodge it as it moves, stay in the top-right corner and watch the direction that the nose moves in first. If it moves left first, immediately drop down to a lower position on the wall and then jump back up after it's vacated the corner you were in. If it moves right first, stay up in the corner until it bounces off the wall below you, then drop down until it's bounced off the right wall again before climbing back into the corner. There are a few different times when you can attack it during this, though I find it easiest to fire as I drop down from the corner.
While all three parts are alive, Rangda Bangda's attacks are fairly random so watch the eyes and walls carefully to see what it will do next. Once one eye has been destroyed the other will almost always use red attacks. If both eyes are destroyed, the walls will close in permanently until the nose is destroyed. If the nose is destroyed before both eyes then the walls won't close in anymore.