I think your main tools here are crawl, ftilt/dtilt, nair/bair (for clanking projectiles if you're in the air as well as easy edgeguards), and dash attack/boost grab.
Crawl, when used in conjunction with short hops, shields, and spot dodges, should allow you to get past projectiles. Of course you have to use these carefully and correctly, but playing intelligently is just too much to cover in a quick post. If you do happen to be in the air, you can easily use nair/bair to clank any non-bomb projectiles.
When you finally get near him, you will only have a brief moment to act (unless you both know each other so well you can mindgame with empty hops/approaches/shields). If you are crouching/crawling, a dtilt is your best option. If you can get in close and you think he will be shielding, grab. This will give you a potential conversion depending on DI. If you are still a decent ways away from him (so you can act but his options are too slow), then it depends on whether you are dashing or not. If you are dashing and think he can get in a shield, boost grab. If he can't do anything, dash attack is your only conversion other than grab, and I like dash attack's followups better vs Link. Finally, if you are not dashing but are at the correct spacing for an ftilt but he cannot act, then do so to launch him for more ftilts (at low %) or a finisher (at high %). If he has time to shield or dodge while you are standing outside of grab range, you didn't actually get in during a vulnerable window. Try again. Do not pass GO, do not collect $200.
One thing I like to do is charge my needles whenever an enemy Link camps. If you can hit them with the needles enough times, the opponent will likely start approaching you, at which point it is easier to find a way through the projectiles. Remember his Hylian Shield will block the needles when he is standing or walking, but not running.