Match one!
I would exploit projectiles a little more, especially since Doc isn't the fastest and usually can't react and punish your lag. You should definitely be pulling Bombs every time you have an opening, and I'd even go as far as to replace a lot of your backward wavedashes with shorthop Boomerangs. You can jump forward to get the sweetspot hit and start a combo, or backward to force an approach that you can counter with the nair or a jab or the like.
You seem a little tentative on the counterattacks. If he hits your shield or whiffs a big attack, go for the pogo. It's fairly fast in terms of startup and it's not that hard to hit with. It also does a lot of damage and has enough knockback to be difficult if not impossible to punish when landed, and can set up for a juggle of some kind.
If you noticed your opponent wavedashing around a lot, throw out a grab. Link's grab is slower than most peoples', but it's still a few frames faster than wavedashing.
Your shffls are a little high. Lower the height at which you start your fairs and you won't get grabbed as easily. Lower the height at which you start your nairs and you won't get punished for the low knockback, and you'll have more time to use a follow-up.
Also, know your recovery. If he misses you on the ledge, try dropping with a nair or even a pogo if you're feeling daring. No pun intended. Fountain of Dreams has a wall going down the whole way, so you should be okay on the recovery.
If you notice him trying to bair gimp you, try airdodging back, smacking him with the Hookshot, tapping A immediately then fastfalling and clipping him on your way up with the Spin Attack. From there, you can get back onto the stage and edgeguard, edgehog, or go back down to gimp him.
If you catch him in a utilt, awesome. You can hit him with a few of them, but watch him carefully. If you think he's about to break out of the juggle with a tech, DI or attack, finish it off with a pogo instead.
The Spin Attack is awesome as a punishing move or something to start an edgeguard, but it's not a very good edgeguard, especially with someone with a recovery as easy to sweetspot as Doc's. Go for a nair airguard or an ftilt instead.
At closer ranges when there's a pause in the action, jab. It's relatively fast and outranges anything Doc has, and the third slash is a gentleman like stab, which clears him away and makes it difficult for him to punish.
If you're going to jump back onto the stage, do so with an attack like the nair, otherwise it's cake for him to hit you out of your recovery. Don't forget about your hookshot, it rarely hurts your recovery. Use it to stall out an edgehog and clip him with the Spin Attack on the way up if he's not refreshing ledge invincibility.
Wavedashing with Link is cool and all, but don't forget that you should be moving for a reason. Don't wavedance when you can dashdance, and make sure you're in the right position to hit your opponent. Also, don't wavedash away when you can smack him with a Spin Attack.
When Doc is bthrowing you, DI up. Pretty self-explanatory. You should never be caught with bad DI from Doc's bthrow. Ever.
If you'll notice, a lot of your deaths are from gimps. Position yourself so it's harder for him to knock you off. Try to put yourself in the center of the stage and force his back to the edge.
Space out your fairs a little more. You're hitting too close to the base of your sword and Doc is able to trade hits with you.
Wallteching would be cool.
If Doc is spamming pills at you, try doing what Aniki does. Back off and shoot an arrow at him.
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