Mega Man X3
The characters in this game include another set of 8 robots. Bit and Byte interfere at certain points in the game, but their initial incarnations are more likely to be found in the Mega Man X main character page. Sigma isn't responsible for the Maverick outbreak, though the intention of their leader, Dr. Doppler, justifies the means.
While in the air, he'll execute a 45-degree dash downward, ramming X with his stinger. Also, he'll throw 5 smaller hornets towards X, them populating lots of space; if one makes contact with X, they'll cling to him, scoring multiple hits. As this is going on, he'll be flying around in an 8-pattern. When damaged enough, he'll send out a small target to seek X; if targeted, small hornets will fly at X. At this point, Blast Hornet will protect himself with a shield of circular hornets.
Most of the time, Blizzard Buffalo will be dashing back and forth in the confines of his long chamber. During his dashes, he can catch X on the horns of his helmet, ramming X into the wall. To impede X's movement, he'll loop three ice globs at X, each forming into an icicle when they hit the wall or floor. At any time, he can unleash a really big, powerful ice beam forward. When damaged enough, he can power up, pulling off invincible dashes.
In no particular order, he has 2 main attacks: (1) He'll throw 1 or 2 balls of energy, each bouncing around the room, or (2) He'll dash at X, uppercutting him with the spikes on his head. When damaged enough, he'll create a black hole on top of the screen, it limiting X's movement, damaging him if he comes in contact with it. At this point, he, too, can pull off invincible dashes.
Most of his movements involve taking short sliding dives towards X. He'll make 1 or 2 acid bursts hover around the room, dripping acidic drops downward. When he chooses, he'll turn himself into sludge, disappearing from site and popping up somewhere else—he's invincible during this period. When damaged enough, he'll gain the ability to throw multiple bouncing acid bursts.
Volt attacks by taking short bouncing dashes at X, sliding across the floor when he lands. He'll shoot out electrical sparks that move along the walls and ceilings, keeping X grounded. When damaged enough, he'll channel electricity from a ceiling generator, surrounding himself with a shield of electricity, sending tiny sparks flying everywhere. Only the right weapon can damage him during this period.
Crush Crawfish will run towards X, trying to catch him in his huge claws, sapping him slowly of his energy. If far away, he'll throw his claw forward, trying to catch X and bring him forward. To keep X grounded, he'll throw small eels towards the wall, them moving up and down, knocking X to the ground if contact is made. He, too, has the ability to dash—I think all the bosses in this game have dash moves.
Speaking of dashing, two of his attacks involve lunging towards X: (1) He'll create 3 drills that blast towards X after Rhino dashes, creating a large obstacle for X to jump, and (2) He'll put his drill forward and dash at X, trying to ram him into the wall. When damaged enough, he'll power up and pull off some invincible dashes.
Neon Tiger jumps back and forth, clinging to the walls of his chamber. At any point, he'll stop and blast X with his ray splasher. When on the ground, he'll dash forward, taking huge claw swipes at X, them with the power to send X into the air; he can use that same claw as a shield. He, too, can power up, taking invincible slash dashes.
Godkarmachine O Inary
Since they couldn't beat X earlier, Bit and Byte combine their power to become this thing. It always stays positioned on the right side of the room, so its size isn't a problem. Its first attack is to whip out a beam sword and start swinging it, creating a scrolling wave of energy; once it hits the wall, it breaks into 2—one going up, the other down. If X is clinging to wall, the top part of it will rise to his level before swinging the sword. Its second attack is to throw its hands at X, one after the other. If the first one hits X, it'll grasp him, ram into the ceiling, then hold it so the 2nd one can nail him. If the first one misses, the second will go along its regular path. If X tries going behind it, it'll rapidly blast X.
Vile is back, and he's angry. He'll start out by dashing back and forth, trying to crush X with his Robot Ride Armor; after hitting a wall, it takes time for him to recover. Secondly, he'll loop little spikes into the air, each crashing down and zipping up, creating a wall. If X gets behind one of these walls, he'll have to blast it quickly, lest Vile will ram his way through it, X with it.
Now deprived of his vehicle, Vile will attack similarly to how he did in the first game. He has 3 separate attacks: (1) He'll blast a flame out of his shoulder-based cannon, it moving along the ground and up the wall, (2) He'll jump into the air and shoot a spread shot downward, from left to right, and (3) He'll jump into the air and try a confined spread shot—only these stick to the ground, X getting stuck if he walks over one. He'll then be open to a Vile attack.
Doppler attacks in a very predictable pattern, though that doesn't make it any easier. After making sure to power up fully, he'll twice try to blast X with three electrical blasts. After completing the 2nd set, he'll begin recharging his energy rapidly; X has to blast him equally as rapid during this time to stay even. Next, he'll power up, rise to X's level (staying grounded if X is grounded), then attempt a powerful dash; the time he takes to recover after doing this is crucial. After recovering, he'll start over again, recharging his power, using electrical blasts, etc.
Sigma Body #1
Sigma's attacks get more and more vicious as he's damaged. He'll start off by rapidly blasting X with fireballs, high and low, blocking X's attacks with his shield. After each flurry, he'll jump to the other side of the room; if X is grounded, he'll stop midway and shoot a rapid downward attack. When damaged enough, he'll do the same fire attack, this time throwing his shield like a boomerang to end it. When in danger, he'll do the fire attack, this time having his shield do a double loop—in case X is clinging to a wall.
Doppler created the ultimate body for Sigma. A lot will be going on during this battle. Sigma will alternate between 2 attacks: (1) He'll shoot a bouncing projectile, it traveling around the room for a limited time, following it up with a missile barrage attack—X will then have to dodge the bouncing projectile, Sigma and the missiles; (2) After landing from a big leap, he'll try to trap X within a wide spotlight-like ray, draining X's energy rapidly. During all of this, the very top of his head is his only weak spot.