So you finished off Bosspider and instead of a nice upgrade as your reward all you got was another lousy Sigma stage. If you haven't noticed, the Sigma stages are meant to be the hardest by pitting you against a combination of the various challenges that you had encountered in separate stages. By the time you finish the game, you should have little trouble with any of them.
Stage Start
Rangda Bangda
A giant face, Rangda Bangda is an end boss type that has been around since the original Mega Man games. As you enter the room you'll notice that it looks normal, having two eyes and a nose. This face, however, is made up of four parts: three orbs or eyes and a nose. By destroying one part you'll take Rangda Bangda's health down considerably. The only way to destroy it completely is to defeat every part.
The orbs are more easily destroyed than the nose. The blue orb tracks your position and attempts to collide with you, however it moves from point A to point B with pauses inbetween. The green orb will appear in one of the eye sockets and fire projectiles at you. Most difficult of all is the red orb, which is a combination of both the blue and the green: it attempts to ram you while firing too.
More simple than the orbs, the nose will transform into a mobile, small robot that bounces around the walls. The trick though is that when it becomes active the two walls will close into the middle area, disabling you from walking on the ground. Stick to the walls if you wish to survive. The nose will choose a different path each time, however it's fairly simple. It's first movement is always diagonally upwards, however the side that it chooses is random. After that it's up to you to estimate where it will bounce and where you can safely hide and fire at it. Oh, you forgot that you had to kill it? Make sure you utilize every moment for a good shot.