Hey guys, I got asked to come over here and give my perspective into this matchup (I'm a fox player), so here goes.
First of all there's a lot of talk here about using heaps of projectiles to get into foxes head and make him waste time reflecting, or to condition him to reflector when he shouldn't giving you a free punish. This CAN work, but its not something I'd want to rely on for this match up because its not something that will work on everyone. First of all if fox is actually getting the reflector off on projectiles, he can of course instantly cancel the reflector into a jump spot dodge shield or roll right after the projectile reflects, its instant so forcing him to reflect your projectiles shouldn't, in theory, put any pressure onto fox since he has so many instant option right after, sure it can distract him a bit and pull his focus away from neutral game, but it shouldn't ever put you into an advantageous position unless the fox screws up pretty bad.
Thats of course for the foxes that use shine, I dont, fox has a much much better tool to beat links projectiles, speed.
At long and medium range this wont seem to be that bad, but at short and mediumish short range, using projectiles becomes very dangerous, I have played against links a lot and if I see them start to use a bomb or arrow, I can quickly move over the projectiles arc (or in the case of bomb pull just straight up run at you because its a little slow) and punish before your recovery frames from using a projectile finish. A smart fox will barely use the reflector at all and will instead just move and use speed to get through and punish you, so you have to be absolutely careful and smart with projectile use, you cannot just throw them out to make a wall like you might on others because it will not keep fox out.
What you can do is fire arrows midair while he is on the ground. Even if Fox reflects, the arrow won't hit you when it gets redirected. You can also shield yourself immediately after throwing the projectile to block (although you won't have time to do this on a reflected fully charged arrow or a close range boomerang).
stuff like this can seem good and might work, but again if the fox player is playing smart or knows the matchup, he can just do things like run under your arrow and wait below you, if you are in the air and fox is below you, you are in a very bad position. It can be very easy for fox to punish your landing if he's next to you. Also uair is very very fast, so although your dair beats his uair, it can be tricky to do because you have to time it just right, and if you throw it out just for the hell of it, he can simply jump up beside you and bair you, and that can often be a kill (especially if you've used up your double jump in the air already)
Shielding is something you have to be careful of aswell, fox has great shield pressure so if you get caught in your shield you need to be very careful. Foxes like to land behind you with a nair on your shield and then pressure with utilt, rolling away in between utilts can work but dont rely on that alot since if fox is expecting it that can be a free punish for him. jumping out of shield can work a little better since you still have a few options after jumping, but then you can still be in the bad position where fox is below you. if you can get a feel for how many utilts he likes to do, you can beat out the utilts with UpB out of shield, but if fox is at low percent he gets a free heavy punish on you of course, however, fox is incredibly light so the percent at which you can safely do this shouldn't be too high. I've seen shorthop dair out of shield work on foxes utilt spam but its tricky. Also you have to think quick because if you just stay in shield fox can turn around grab which comes out very fast.
As for dash attack on shield, dash attack is a great setup for a lot of foxes kills, so you might find that a lot of the time, when you are at high percent, fox might start spamming the **** out of dash attack, especially if he is feeling any kind of pressure and really wants to get that kill. As mentioned above, it can be tricky to deal with the dash attack, but UpB out of shield is an option that can win you matches. You are both high stock last percent, fox is just spamming those dash attacks so you see them coming easy, you shield it and then UpB out of shield and thats it you win. If he is running at you from far away and you just KNOW he's going to dash attack, bring up shield but then before he hits you, jump out of shield and come down on him with a dair. This is incredibly risky, but if timed right (and he was going to dash attack) will catch him completely off guard and wreck him.
other then that, you just gotta play careful and smart, I know thats cop out advice because it doesnt really help out much.
Watching some fox videos can help you to get a feel for foxes strings and what foxes like to do after getting grabs, knowing that can help you be prepared to avoid or beat some of it which can help a lot.
Also, once you get fox off the edge, you need to use your projectiles to stop his side B and double jump and force him to have to recover from below the level with his UpB, once you do that, your options for gimping him open up a lot, since his UpB is very very linear. If you can get the hang of doing this, you can make the match up a lot easier for you by getting early kills to make up for all the insane **** he can do to you.