Typing as I watch
Are you Link or Fox?
I'm mainly going to focus on Fox here, since I play Fox a lot more than I play Link.
For starters, USE SHINE! It comes out in one frame (ie 1/60 of a second), and can be cancelled just as quickly by jumping. It's the fastest attack in the game, and great when your opponent is right on top of you (as Link is quite often in this match).
Fox also depends heavily on the dash attack, which is probably his single most easily-punishable attack. When rushing in, it's generally better to cancel your run by crouching, then pull out a tilt, a smash, or a shine.
Link: this is a minor thing, but try using Up-B on the ground as a ledge-guarding move; hit fox with that, and he's pretty much fucked, even at very low damage.
Another thing -- and this is something it seems both players could work on -- is following up on your attacks. That is, after you nail your opponent, don't sit back and wait for them to collect themselves and attack again -- chase them down, and keep comboing them as far as you can.
Fox's play seems to pick up as the match continues, though he still doesn't cancel his shines, and depends too much on roll dodging to get around. Some characters can be played pretty well without wavedashing, but for fox to be anywhere near the top of his game, the player needs to be able to wavedash; it provides much greater meneuverability, improved speed, and best of all, much less predictability.
Another thing for the fox player to work on is short-hopping his aerials; there are a number of instances where fox does a full jump at close range to come down with an aerial; this is much slower and thus much easier to counter than a short-hopped aerial. Of course, short-hopping is significantly harder with Fox than with many other characters, so it will take some time to master.