Okay, I watched your movie, and if you're really serious about this, you need to do a little more research and take a lot more time. 444 rerecords is not enough for a movie of that length, especially in a game like this. The goal of a TAS is not just to get to the end while looking basically good, it's to be as fast or as entertaining as possible. That's going to take more work than what you are putting in.
For research make sure you watch the runs already available, as well as listen to the commentary I posted on mine. The link is in the forum and it has good information that's not available through just watching my run. Also read the entire 2p expert thread, where I was posting the WIPs for my run.
As for specifics of the run itself. You need to optimize movements a bit more. If an enemy is about to block your path, shoot it out of the way, for example. Make sure that on bosses, you have the gun damaging them on every single frame, or at least every single frame possible. There were lulls in many boss fights that were not necessary.
You also take damage much more often than you need to, and there were many times where the damage you took wasted time.
Gunstar Heroes is a game where slightly different actions can change your luck a lot. In other words, you should not have had to wait as long at the first bird to get the upgrade you wanted.
Bravoo Man should be body attacked. Any time when you can body attack a boss, you should. It does much more damage than the guns and more than make up for the few dead frames.
Halfway through the Pink battle, you start hanging from the cab and that's obviously a much better choice. I I were you, I would have gone back to the beginning of the fight and seen if I couldn't just do it the entire fight (also, try testing body attacks)
The last enemy on the first train can be killed before the train returns. You would know this if you had been watching my run carefully.
Because of the gun mechanics, there is no reason why any of the Seven Force battles should take longer than the ones in my run. Yet a few of them do. Again, the answer lies in always having the gun pointed at the enemy. On a couple of the forms, you use flame, which only does 3 damage a frame, which means that it's suboptimal.
The phantom in Orange's stage can be body attacked.
In the smash fight, you neglect to body attack him right before he flashes. That could have saved many frames.
Whenever you get a chance to throw Orange from the air, use the drop glitch. Don't actually throw him. That's slower. Also, take advantage of the animations where you can body attack him. Watch his health, you should have been standing inside him for that last throw so you could get him on the first frame possible.
Try body attacking that gun in Black's stage.
Also, you might want to rethink the guns you use on each boss. For example, the best gun for Papaya Dance is probably double flame. Bravoo Man may be flame chaser or double force if you can haggle it. Pink is probably the flame saber or flame chaser. For Seven Force, I would go double force all the way.
Keep in mind that there is a good chance this run may be rejected, especially if it doesn't add anything new or beat the currently published run.
