Anything undead or from Lovecraft's Mythos.
I see anything that falls into either of those categories and I will immediately fail the horror check, the combat check AND the flee check, and die of a heart attack right freakin there. (why yes, I HAVE been playing Arkham horror!). And maybe the Joker. That...would be unpleasant.
Oh, and a thug, or gang of thugs would be pretty bad too, or a very large and hungry dog. But that's not heart attack material. That's only wetting my pants material.
I wouldn't mind meeting the Dark Knight himself, though. I'd just give him a thumbs up and say "Yeah, I know you don't do autographs, so I won't ask. Just keep kicking ass, Batman. I didn't see you here."