I'm going to mention some recent tricky roles.
So first things first, Evan Hansen. Not only do you have to act awkwardly and learn all of the little ticks and fidgets he does, you have to literally sob on stage while you're singing. You need the right amount of emotion to make the audience feel bad for him. You need to study up on mental illness pretty extensively to get this role right, have incredible range, and basically transform into another person. Evan is as close to real as a character can get that even Ben has sort of adapted Evan's characteristics. All the praise for Ben is well deserved; this role is by far one of the trickiest to get right.
Now these two aren't the hardest out there, but are pretty hard to perfect (from what I've heard by others and seen myself): Donny Novitski and Julia Trojan. Hear me out. Donny has to have stage presence. Not an incredible amount, but it needs to be nuanced yet desperate. Donny has PTSD, and the actor portraying him has to portray that rawly. Not a very easy role to cakewalk. Julia, while she doesn't have a mental illness, she does suffer from grief surrounding her husband. She needs to slowly open up to the band, and have that warm, loving personality. Plus, both leads needs to have silky smooth voices that have the vibrato to slay the h*** out of that score. The dancing and choreography is also a prominent part of the show, so there's that. Donny also has to play piano.
A tricky one that doesn't get discussed much is Dolly Levi. Not vocally, because measured by only that it's a piece of cake. But the personality has to be there. The explosive chutzpah, the creativeness; you don't want to phone in the character. I've seen some Dolly's that just can't get into the role because they either overplay it, or are way too subdued. You also need to be feeling emotion in her monologues. Dolly has to be reminiscing in those moments, and hamming it in with excessive tears isn't the way to go.
The D'Ysquith family. I don't think I really need to say why.