I want to say no, because the mission with kerrigan and the medivacs and the three control tower thingies (the mission where you race kerrigan for a research disk or something) seems to not give you enough time, but I can't remember. I think i may have killed almost everything (or did so, i can't remember) once on casual, but that's the only one i can remember now that would be hard. I've done it on a lot of the easier mission where you're not expected to. (i.e. devil's playground, the dig, the evac, zero hour, and welcome to the jungle, and maybe some other ones) I've always thought this would be so cool. I think on zero hour i once had full map control, even in the last ten seconds when the things drop from the air that become tumors by having clusters of marines where they fall
For some reason, if i treat playing the computer as playing someone else, my macro practice kicks in. and missions become a lot easier than when I play the campaign as it expects you to.
Oh, I think maybe great train robbery would be hard. I just haven't tried enough things on casual. Hm, also, in utter darkness might be hard, but I think the spores on the edges are rebuilt? Idk, but I think structures that are rebuilt by things outside of the map should not count.
I mean, once you learn to be efficient in one v one matches and killing enemy bases, it's not so hard to kill enemy bases on normal or even hard (disclaimer, maybe it's hard on some missions, it's been a while)