Mega Man X/Sigma Stage 1

Sigma Stage 1
Finally, the final areas of the game. In the first Sigma Stage, you'll encounter Vile, Boomer Kuwanger (back for another fight), and Bosspider, who's a fairly simple boss. If you didn't get the Buster upgrade from Flame Mammoth's stage, you'll be able to get it from Zero later on in the stage.

Stage Start
When you enter this stage, Zero will be waiting for you to give you some words of advice before splitting up.

Head right and take out the Mega Tortoises, use Chameleon Sting or Storm Tornado to take out the airborne enemies.

When you reach the cliff to the right, prepare yourself for some close calls. It's recommended that you use anti-air abilities like Chameleon Sting or Boomerang Cutter in this section. For this part, you have to jump from each flying machine until you reach the top while dodging those annoying purple flying robots. If you're having trouble getting to the top, you can use the Rolling Shield's alternate fire (or even Chameleon Sting), which will protect you from all forms of contact.

Once you reach the top, you'll have to deal with some cannons and Mega Tortoises. When you get past them, keep climbing up the ladders until you reach the top, where you'll then have to fight Vile.

Armored Mech Vile, part 2
This is another storyline battle, so just keep getting hit by Vile until he shoots one of those glowing orbs. Once he does, you'll be disabled and unable to move. After the cutscene, the real battle begins.

Vile
Vile will be a pushover with Rolling Shield, which does tons of damage against him. His only attacks are a projectile that will make you unable to move (in which he'll then attack you) and an aerial jump where he rains bullets down on you. You can dash past him when he jumps, and if you're stuck, just keep dashing as best you can. The Rolling Shield will make quick work of him, and he leaves himself open a lot, so you should be able to kill him with no problem.

You can also get the Buster Upgrade after defeating Vile if you haven't gotten it already.

Mid-level
After the Vile fight, you'll have to get across the next area by jumping on various springs while dodging the laser trip wires from Boomer Kuwanger's stage. Wait for them to disappear and then quickly jump on the springs.

Afterwards, there will be an annoying wall scaling sequence. You have to constantly dodge several enemies while scaling a large wall... but to make your life easier, just use Chameleon Sting's alternate fire, which will make you invulnerable to all attacks. When you get to the top, prepare to fight Boomer Kuwanger.

Boomer Kuwanger
Use the same strategy as before: shoot him with his weakness, the Homing Torpedo, while hiding in one of the corners, and then dash to the other corner if he tries to go underneath you.

Final Area
In the final area Mettools and Spinies will try to make your life more difficult. Use the Chameleon Sting's alternate fire to safely make it across, and then step inside the dungeon to fight Bospider.

Bospider
This is a fairly simple boss fight with Shotgun Ice. Bospider only has two attacks: he'll try to crash into you or he'll release four miniature spiders which will try to hit you. He tries to crash into you when he's near the ceiling; he'll then try to find the easiest route to you by moving across the beams in the room. The top beam is where he'll start and the bottom beam is where he'll end up going, so pay attention to where the bottom one is so you don't get hit. When he touches the floor, the red eye on his back will open, which is his weakness. To avoid getting hit by him, it is recommended that you stand under him when he's near the ceiling so he moves directly towards you. Once he gets close, dash and then shoot his eye with the Shotgun Ice. If he drops the spiders, either jump over them or destroy them with the Shotgun Ice (it has plenty of energy, so don't be afraid to use it if you have to). Repeat this strategy until he's gone.