With Link, you have a vast array of projectiles including your arrows, boomerang, and bombs which can be used against your opponents to create openings. Shulk is a difficult character to face against especially if your opponent knows how to use monado arts, which is deadly. Try to keep your distance from Shulk, as spacing and projectiles is the key for Link's neutral game. Even though Shulk's f-tilt and u-tilt are fast, his aerial game isn't because of how long it takes for the hurtboxes to come out, making him easily punishable with close quarter attacks from Link. His nair and bair are also good attacks, so be cautious from them.
Buster art can rack up a lot of damage quick, which is why you have to be cautious when going up against Shulk with this art. Use projectiles and spacing in order to zone him out, especially when you're at low %. Since all of his moves have lower knockback in this form, it's easy to punish him.
Jump art is only ever used during recovery, or as a way to gimp you offstage which is rare. You shouldn't have to worry so much about this art.
Speed Art is used as Shulk's combo game since the knockback on his attacks are decreased. This goes hand to hand with his speed and can allow him to rack up combo's against you. Again, spacing and having neutral is key, but one thing to keep in mind is that he has decreased jump height.
Smash Art is used by him when you are at a dangerously high %. Shulk has decreased damage but increased knockback with his moves, so be cautious. Avoid all of his smash attacks since they launch you further when you're at a higher %, and both his nair and dair are deadly in this form. It's easy to punish him when you're at a lower % since his moves have decreased damage.
Shield Art is used only when a Shulk is at a dangerous %. In this form, he has increased resistance from attacks and has a bigger shield, but is overall slow in the air and ground, and has reduced jump and kill power. It's a little more difficult to face off against Shulk if he uses this at early %'s, since he has higher resistance which prevents combos against him.