Just to summarize quickly, I feel Shulk has bad matchups against pretty much every other sword character against Lucina and Roy, where I feel he has a slight edge, and the Links and MK, who are probably roughly even depending on how he plays. The main issue is getting outspaced.
Marth has much better frame data and the tools to disrupt and avoid our finishers, as well as edgeguard us and scare us with his tippers. His slight range edge and kill power advantage over Lucina make it hard for Shulk to get mileage.
Ike and Cloud are better in every dimension of gameplay except mobility with the arts. They have quicker attacks, better finishers, better aerials, better hitboxes with more coverage, better spacing tools and 50/50's, more consistency, and Cloud has limit while Ike is heavier and has a better recovery to boot.
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Corrin can literally shut Shulk down with his counter. I found this out the hard way. None of Shulk's approaches seem to work on Corrin, because his poor start-up frames allow counter surge to trump him every time. I never lose to lv9 AI, but the first time I ever lost a free for all, it ended up being me vs Corrin, and even though I was up a stock, the AI counter surged me every single time I attacked (this was post patch, too) and outspaced me with Fsmash when I tried to grab. I got killed by the Corrin counter twice, and couldn't win the game. Never felt so frustrated before.
Shulk NEEDS some kind of legitimate improvement. Not damage buff band-aids or landing lag decreases. Legitimate auto-cancels, more range, better all around frame data, tweaked finishers, or any combination thereof. As he stands, he gets beat by anyone else with a sword (even MK, Links and Lucina can be a struggle) because he simply lacks the tools they all have. I think Corrin might be Shulk's worst match-up as a whole because he can wall Shulk out with DFS, punish his approaches with DL/IP and Forward Smash, and block any incoming hits with Counter Surge. Seriously, I can beat Cloud, MK, Diddy, Fox, Sheik etc. all being played by lv9 ai, but I actually got two stocked by a lv9 Corrin. After more than 80 hours of practice.