Pretty sure (correct me if I'm wrong) that Robin's d-throw can link into his jab or u-tilt at low percentages.
Robin's not going to get in our zone and that's not her main objective anyway in the match-up. All she needs to do is to keep Shulk away with her projectiles and her disjoints, and it's really difficult to get into position against Robin. She beats us out at long-range and even if we're suppose to get in, she still beats Shulk at close range since her moves come out faster. Your best bet against Robin is to go at mid-range against her. From a certain distance where your aerials' hitboxes will probably reach Robin (whether she's shielding or not), that's exactly where you should be. From that distance, you can decide whether to play it safe and space from that distance, or commit to an approach option (N-air/cross-up n-air or RAR b-air), or go for a quick dash grab (stay in speed art if you're planning to do this).
You're gonna be in speed art for a lot of the match-up. I'd love to say that jump art is useful but its falling speed and horrendous defense nerf makes it a risk to use, even if the concept of jumping over projectiles seems cool but by the way, that really comes off as predictable to be honest. You might eat a u-air on the way down if you're too antsy with your jump art approaches. Speaking of jump art approaches, Shulk's approaches (in general actually) are rather predictable since it all comes down to (assuming you're approaching from mid-air since this is jump art we're talking about) n-air or FF > grab or jab. Also, jump art turns you into much more of a combo bait than usual and Robin hits hella hard. Buster art only comes out when you feel like you have the upper hand in the neutral but you're probably going to get timed out once the Robin player manages to return to the neutral. Same can be said for Smash art. Shield art is situational as always. Its uses at low percentages against Robin, I'm not really sure if it helps with escaping her early % combos (probably does) but it doesn't matter anyway since most competent Robin mains will probably just run away/camp if you active shield art. Basically, shield/buster/smash are susceptible to being timed out because Shulk's mobility without jump or speed art is mediocre.
Another thing to note is to never stay above Robin. It sucks to be juggled by Robin's ridiculous u-air. You can't contest that **** with any of your aerials. Like, you can suggest d-air but it comes out waaay too late for it to contest u-air so it's probably not going to work most of the time. Jump art is a viable option though for escaping Robin's juggles. Also, if there's anything you want to exploit in this match-up, it's Robin's horrendous recovery. It sucks. Go ham with jump art off-stage and edgeguard Robin