Hey guys, i'm a fellow Shulk main on these boards (he's my primary, so i'm pretty knowledgable on how he works, and what are his strengths/weaknesses against most of the roster), and i was just strolling across the forums for characters that i use on/off as secondaries and the like, so i figure i could spread some knowledge on how to deal with Shulk as Lucina. Granted, i admit that most of the time in these match ups i'm the Shulk rather than Lucina, but i'll try to use my knowledge on Shulk's strengths/weaknesses against Lucina to better help you Lucina mains take him on.
First, i'm going to talk about the edge guarding portion before i get to dealing with Shulk's neutral game. For all intents and purposes, i'm going to talk about Shulk heavily with his Monado Artes, given it's the core/main part of what makes him a viable character and what makes him challenging to deal with, so Normal Shulk (one who doesn't have an arte activated in any point in time) will be touched on, but not often. When i reference his Monado Artes, i'm putting their names in the text in their respective colors to make them easier to identify to those of you who don't know Shulk's buffs that well.
A good Shulk can be tough to edge guard if they use Jump, although they may not always use it due to it being risky for them as they can easily mess up the input and get a diff. arte or do a special early and lose a stock from this. If he's in Jump, there's a pretty good chance he'll return on stage, if he's not using an Arte, it's still somewhat risky to edge guard him as he has more range over Lucina, but if he does try to bat you away when you try to edge guard him, you can easily make sure he stays off stage if you predict and counter his attacks accordingly. Now when Lucina is being edge guarded by Shulk, that's a different story. His range is definitely good for this, and typically when a Shulk gets you off stage and goes into Jump/Smash, they're going in for the kill, and their augmented stats make this really hard to combat. Best thing to do is to air dodge accordingly/counter if you can, as while he is good at this, his attacks are relatively easy to see coming. One last thing, watch out for Dair. Shulk's comes out pretty slow in comparison to other spikes, so if you air dodge too early, you may dodge the first hit, but the second will definitely hit you and KO you. Even if only the second hit lands and it doesn't spike you, it can easily send you flying away from the ledge again and KO you regardless.
Now for combating his Neutral game. Right now i'll go over his basic attacks and combos, and i'll have another section talking specifically on how to deal with the Buffs he gets from the Monado Artes themselves as that will be the biggest obstacle Lucina will have to deal with when fighting him. Given that Shulk has no projectiles, it's obvious that since the two of you are the same in the aspect, you both will have to get up close and personal. Difference is, a good Shulk will utilize his extra range and Monado Artes over you to take you on. His grabs are pretty good and lead into alot of his combos, such as U-Throw into U-Tilt (and even Up special in some cases), D-Throw into F-air (if spaced right), and B-Throw into Back Slash (depending on if Lucina hits the ground after the attack or not). His Tilts are long reaching, U-tilt is great for anti air but cannot hit very well to Shulk's side, D-tilt is another tilt that works well with Grab combos, and Side Tilt is great on his end for pivots and can be used as a viable KO option at higher percents. As Ffamran said above me, Shulk's smashes are strong but very laggy and punishable, most often times if you're fighting a good Shulk, the only Smash attack you'll be able to punish more often not is D-Smash, which has 3 hits that you need to watch out for before Shulk is completely vulnerable to a punish. His F-Smash/U-Smash both have 2 hits if the full attack connects, and the range on them can be used to punish with the second hit if spaced correctly, while D-smash has alot of range and KO power. His Aerials are also ok, U-Air is easy enough to dodge honestly, F-air is a decent approach tool and good for edge guarding, B-air has the most range of the aerials and is one of his KO moves, D-air comes out a bit slow but strong, and N-air is Shulk's best aerial for combos, as he has little landing lag when used in conjunction with fast falling to the ground. His specials are pretty situational overall and laggy. His U-Special is Air Slash, which looks basically like Lucina's dolphin slash, but has a second hit that he can use to deal damage, and can be good for KOs at later percents. Back Slash is pretty laggy and risky for Shulk to use, which is good for punishing him should he use it. It has great range though, so don't underestimate all the time. Neutral B is Monado Artes, which i'll talk about later. And then there's his Down Special, Vision, which is his Counter. It is pretty strong, arguably one of the strongest Counters in the game, and when used with his Monado Artes can do alot of damage/knockback to the opponent, so this is a move you want to watch out for.
Now for the M-Artes. Shulk has 5 of them, and for each strength they give him, they also have an exploitable weakness aswell. Jump gives him amazing speed/manueverability in the air, but really low defense and it's easier to deal alot of damage/KO him in this state. Usually it's used for Recovery, Edge Guarding, or just approaching Lucina with aerials. This typically isnt' good/useful for him on stages with platforms as they stop his approach pretty well, so you might not see this on every stage. Speed gives him, well, speed almost on par with Sonic, but lessens his overall damage output by alot. Usually this'll be used to grab/pivot grab, and is arguably the hardest Arte to combat. Usually this is used at the start of a match to rack up damage from 0-40% with grabs. Best thing to do with this arte is try to avoid him by timing your jumps so at the very least you can dodge his aerials and not get grabbed. Shield gives him great defense and makes him harder to KO, but makes him slower than even Ganondorf. You can exploit this by trying to get him off stage or comboing him due to the low amount of knockback he has in this Arte. Buster lets him deal alooooooot more damage and does less knockback, making ite asier for him to combo. It's typically used either to comeback from the losing side of a match, or immediately after Speed. Shulk takes more damage in this Arte, but not as much as he does in Jump, TBH, best thing to do is try your best to play it safe and not get hit by his attacks, as he can rack up your damage to 90% or so if he overwhelms and combos you. Counter works really well here, as since he does more damage here, the counter calculates that and artificially increases knockback aswell(i think this goes the same for Lucina as it does Shulk, this might only work for Shulk though, so sorry if i'm wrong), so at the very least you'll deal alot of damage back to him along with the knockback. Last is Smash, which greatly increases Shulk's knockback that his attacks do, aswell as the knockback he takes, meaning while it makes it easier for you to KO him, he can be KOed just as easily, making this risky at high percents for him. He'll use this basically when you're at a high percent to land a kill, like if he's going for an off screen KO. Depending on your percent and his percent, you should either:
A) Try to avoid his attacks at all costs, B-air, his Side TIlt (this will be used as a pivot more often for KOs), and smash attacks are his primary KO moves in his Neutral game in this Arte, so you want to watch out for them. Also, WATCH OUT FOR HIS COUNTER. In Smash, counter becomes alot deadlier, one good hit if you're at 70% will KO you.
Or,
B) If Shulk's at a high percent when using this, you can try to KO him before he does the same to you. He's just at risk of being KOed as you are at this point, so you can use the power of his Arte against him with this state.
My overall advice on how to deal with Shulk is be vary of his range and spacing, and try to take advantage of the weaknesses that his Artes give him (although, a good Shulk is typically good at not letting the opponent take advantage of his weaknesses for the most part, so keep this in mind). A good thing to note is that Shulk's not very good at dealing with pressure, so if you can get up in his face and not give him much room to breathe, there's not much he can do, as alot of his attacks are pretty laggy compared to the rest of the cast. Lucina has the advantage when it comes to this, she can attack him quicker than he can attack her when she's up close and in range. Always punish his laggy attacks when you can and take every advantage of his Artes weakness depending on them. When Shulk uses an Arte, he's basically forced to commit to the buffed nature that the Arte gives him (Basically it goes like this: With Jump, Shulk's power is all in his air game now, so he's basically forced to attack with his Aerials for the most part, Speed has him mostly sticking to the ground, Shield has him being defensive and punishing more often, and he's more likely to use Counter to get you off his back. Buster forces him to go all in and get aggressive, so be prepared for that. And Smash has him doing the same as Buster more or less.)
Hope this helps! Sorry that it's so long. xD