Frankly, I like Falco. He's my secondary (Link's my first though
). And I have a friend who likes to use Link all the time, so I understand a little of a Falco player's mentality.
Clearly, the Chaingrab to DAir is one of the best combos. You can play some mindgames with a Falco player by jumping later than you normally would to dodge the dair, you can immediately tether, etc, but there is no one way that will get a Link player risk-free back on to the stage, cause Falco can simply drop off the stage and spike, he can short hop and wait longer to spike, etc. So mix it up a little. Tethering really does help.
In a projectile matchup, avoid using arrows unless it's for an arrow lock. Really, I can't tell you the amount of times when my friend has started charging an arrow and I just sit there spamming the shine until he realizes its a losing battle. Don't use boomerang to aid recovery, it really doesn't help at all and often gets in your way, making you an easy kill (aka Falco doesn't have to do anything). Bombs are really stupid unless you're above or below Falco.
Speaking of getting above or below Falco, use stages such as Battlefield that are small and have platforms that will allow you to stay vertically oriented to Falco. Use Utilt, nair, the sliding-Upsmash technique (only when below Falco), and dair to approach and rack damage on Falco. Nair is a particularly effective approach when using platforms, as it is a sex kick that doesn't have specific timing for hits (which Falco can easily beat). It also has no lag at start or end, allowing you to get it into Falco's face quickly and end with quick land attacks such as the standard AAA combo (Jab cancel is stupid because of Falco's shine). Another blessing from nair is the fact that you can repeatedly jump into Falco, dodging his shine and most aerial techniques he would otherwise use to retaliate. Although Utilt is a good technique for keeping/getting Falco vertical, you'll often get hit by Falco's dair and take damage yourself. Zair is a burden against Falco, because he'll shine/blaster you until you approach.
Let me tell you that you'll need those platforms to avoid amazing damage vs. his blaster.
In reality, staying in a vertical position to Falco is key. He can blast'er you to oblivion, shine your non-vert approaches, and shine any and all projectiles used against him. His aerial attacks can quickly break through most of your own, and recovery options are virtually non-existent. Stay in his face and use only techniques that you can get out fast. You'll need to change your entire strategy to beat Falco, but
it is possible.
Really though, I'd give this match 9-1 to Falco.