Here's how Shulk is going to fight you:
You don't have a lot of % ? He's going to use the buster art. Avoid a grab at all cost, because in this form, he has a true combo that deals 50% (and that combo is just down throw + side smash). The buster art is his best tool to make your % explode in a matter of seconds, be really careful with it. On the downside, his attacks have nearly no knockback in that mode, you can punish it.
You have a lot of % ? He's going to use the smash. Be careful, he doesn't deal many % but his attack have crazy knockback with that mode. Basically, a dash attack can kill a middleweight character at 100%. His nair and fair are also dangerous. And of course, avoid a smash at all cost. If you don't have a lot of %, you'll take some knockback but nearly no %. Don't understimate the range of his tilts, it could be fatal. Also, in Smash Art, you can easily eliminate him, he's much more fragile.
Speed Art: Most of the people are bad with it, he has bad jumps and you can eliminate him easily. But be careful, he can combo you really easily.
Jump Art: He's just going to use when his other arts are on cooldown. Or to recover.
Shield Art: He's going to use it when he will have a lot of %, just to give you some % before dying. You basically can't combo him when he uses this art.
Good Shulk are not always using an art, they also play vanilla Shulk. He's strong but not really fast. But be careful, his nair and fair have a good range. Same thing with his tilts. Avoid his back air, it has a good range and it is really strong.
And that's pretty much it !