This game is also available on PS1.
When you get to the second part of Dr. Doppler's lab, there will be some changes if Vile was destroyed. When you get to a robot ride armor platform, get into a F-armor, because when you go down, the level will be flooded. Now make your way to the mid-boss door. Before you go in, switch to Zero and go in to face a mosquito/bug like mid-boss. Have Zero defeat the bug and it will explode on Zero. This will leave Zero highly damaged. He will give the beam saber to Mega Man X. To use it, charge the X-Buster until you turn green, you'll fire 2 charged shots and then the sabre. The beam sabre is very powerful and can kill all the bosses with only 2 swipes, even Kaiser Sigma.
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Note: You have to make it to the secret place with full life.