Sorry bud, I'm a big fan of this game (Capcom Classics Collection Reloaded, yo) and as much as I would like this game on the site, I sadly don't think this run is very well optimized, certainly not enough for publication.
You should take damage more. After you get the option (which is pretty early on) there are several areas where you stop to destroy those buildings where you can have the option destroy it during the uncontrollable animation. The reason you should hurt yourself is because after you take damage your character shoots MUCH faster. This would save a lot of time on the bossfights, which presently aren't so hot because of the gun's lackluster cooldown. Right now the only time you seem to take damage is at the end when you should be in the powered-down form for almost the whole run.
Also why isn't this 2 players? I'm sure that would be faster given the fair amount of twin bosses in this game.
Here, I tried the first stage (1 player). This is how I think a good run of this game should look, it is about seven seconds faster, mostly because of the boss.
https://www.youtube.com/watch?v=Viifm2R39pA
(also you can skip that warning when the game boots up a lot sooner by putting in a few coins but that doesnt really matter)