Argh. Leave the original audio in. It's nice to listen to, and it helps to catch stuff that I otherwise wouldn't notice (imperfect wavedashes and such).
If he's above you on a platform, he's at a disadvantage, because you can attack him and he can't attack you, right? That means you shouldn't even the playing field and make it so that he can attack you. What I mean is short hop uairs at him, don't full jump them.
Good waveland, but after you do it and he whiffs an attack, don't shield. In fact, don't shield at all after stuff like that. He's Mario, not Marth, he's not going to be able to hit you after a waveland when you're spaced like that, and he would not have fired a fireball if you were coming down at him like that unless he's an idiot. That means you're essentially safe, so wavedash/dash in after he whiffs something and punish him. Shielding is just unnecessary lag.
You're missing some L-cancels, so work on that. I'd work on the approach too, you're using some less than ideal approaches (like the dash attack) and neglecting pills in the approach. You can ask some of the other Doc boarders for good approaches (they'll probably say stuff like JC grabs or bairs or something) because I honestly don't know how to approach as Doc either, other than spamming pills and running after them.
After you throw a pill, don't just sit there. Run after if it you think it'll connect or force them into a shield, or throw another one.
At 1:06, there really was nothing you could ledgehop to hit him. So don't try it. Ledgedash or something instead, otherwise you're just asking for an fsmash.
You have these weird pauses after a lot of things where you either spot dodge, shield or stand still. Rely on your hunch and go for it. That's what makes mindgames work - confidence that they will work. If you play a purely reactionary game, you'll always be one step behind, unless you have retardedly good reflexes.
Don't dtilt. Just don't.
Okay, as far as movement goes... you're doing it too much. Yes it's cool to short hop and fly over your opponent or wavedash through them, but you're not attacking when you do it, nor are you invincible, so you're just opening yourself up to attacks.
Speaking of not attacking, the majority of your attacks seem either too early (which will get you shield grabbed) or too late (which will get you pre-empted). So work on the timing.
Your jabs are spaced out kinda far and your grabs aren't connecting. If you notice that happening, just jab dsmash instead.