I reported to a middle manager like that at a Finance company. Whether you're slinging pies or slinging pie charts, insufferable assholes abound.
What I did was I put up with it until I found another job and then I quit, stat. The reason was, I got that Finance job through a "bigger boss" and I didn't want to cause problems for him by going to HR to complain about the middle manager.
And I didn't bring it up to the bigger boss directly because I knew he would probably suggest some kind of sit-down with the three of us or something like that, which I didn't think would work. (The middle manager was the type who would hide his antics if confronted like that—continue to make my life hell but secretly).
If I could do it over, I would have brought it up with my bigger boss but then rejected any offer for arbitration. I would have tried to set my own terms like, "I just know I can't work with this guy, so you'll have to move me, or can me if moving me isn't possible." I don't know what your circumstances are, e.g., if you have to cling to this job or not, but that's what I would try. I think another responder gave a similar response—basically, go to the higher-up manager, but try to go with a plan of action that you recommend, e.g., changing shifts.
Otherwise, I think the default, uninspired corpo solution might be to get you two to talk and shake on it like you're back on a goddamned elementary school playground. And your mileage may vary if you get forced into that.
I took a look at other recommendations here like "playing nice" or "playing ignorant" or "trying not to take it personally." And, yeah, if you have the patience for those approaches, give them a shot I suppose. Just remember that you are being paid to do a job, and its up to you to determine whether "putting up with a Hershey-stain of a coworker" is a fair part of your responsibilities.