I'm pretty sure this is the fastest route through Mega Man X 3. It defeats the 8 bosses in weapon weakness order, starting from Blizzard Buffalo, gets the Air Dash to save time overall, leaves Bit alive so the Bit/Byte hybrid is fought instead of the waste dispenser, and kills Vile for the Beam Sabre. I'm pretty sure for every battle after the Beam Sabre, the explosion animations take longer than the actual fighting ;)

Overall this run is pretty well optimized. Bosses are hit as soon as their vulnerable again, nearly all of the minibosses die in less than a second (I'm especially proud of the Neon Tiger miniboss), and X is constantly moving as fast as possible of course. It was really fun to make, hopefully it's fun to watch, too!

Bisqwit: Moving as fast as possible... maybe.
Progressing as fast as possible? Possible that not.
I think it moves sometimes too much.
I'm not going to reject this submission, but I'll give it some time and wait to see if someone beats it :)