I've always found the durability of the Heracles of mythology to be in one of those grey areas, especially against slashing/ cutting weapons and things in general other than blunt trauma. So it depends largely on where you think he stands regarding certain types of attacks and how fast you think he is. I always thought there was a good reason why he gathered armies of his own to fight armies instead of just wading through them. Depends too, I suppose, on which versions of the myth. Considering Batman's speed and his arsenal of gas and probably some edged batarangs, I'm not dismissing his chances here.
Edit: Heracles' skill with a bow was extreme, arguably even superhuman when it came to accuracy, probably his best weapon. But I don't recall any feats of superhuman speed when it came to firing off arrows so the accuracy probably doesn't matter against Batman who simply won't be there. Of course, if there are objects in the arena and Heracles starts tossing boulders, big boulders...