My observations from that video:
You don't deal with missiles very well. It seemed, to me, like you would shield almost every time he shot a missile, especially when he was further away from you. He was able to take advantage of this to essentially have control over the entire stage.
As for solutions, unfortunately, I don't have experience with the matchup, so everything I say is going to be pure theory based off of those three games and the few games I've played vs Samus. I could be wrong, but I believe PSing the missiles would allow you to act more quickly after shielding them, making it easier for you to approach. Another option is to not approach as quickly. It'd be tough, you should be able to find a safe maneuver between his missiles. Or just get hit by a missile on purpose. You could always do that to help you get into a better position.
Once you get close, you have to always be prepared for a Missile or a Fair. A missile is going to hit you if you're directly horizontal from him, and Fair is just really fast (Hits on frame 4, I believe). You need to always be prepared for these, and play around them. While you'll miss out on hits because of this, he should miss out on more. Once he realizes you're playing around missile/Fair, he'll stop using them, and you can take advantage of that.
Nair and Ftilt also come out really fast. Keep that in mind for whenever you're in that space where he can't hit you with his other attacks, but can get you with those. If you can bait either of those out of him, you should be able to get a good punish.
Everything Sveet said seems pretty good.
Why did you pick PS for the third game? I feel like PS gives Samus too much room to missile, and taking away the top platform gives you less room to avoid them, and that seemed to show in games two and three.