I suspect the "shoot for" isn't the relevant phrase here. It could be any verb, the relevant part is "for shit" - so you could say "he can't sing for shit". It is the same as a similar version " can't x for toffee" - where even with the incentive of toffee a person would be unable to do a thing. The suggestion is that even if a challenge (singing, shooting) was so easy that there was a prize like shit they would fail. That said "can't shoot for shit" is a particular common version of that phrase, just because of the alliteration.

shooting for shit = shooting to get shit or nothing or something of no value. So add that into what I said above. Even if Harley was shooting and there were no rewards involved. He would still miss.

Marlboro is implying that Harley is a bad shot. That he would miss a large target. The suggestion is that "shit" would give off a very unpleasant odour/odor over a wide distance. That Harley would not even hit the "invisible" odour/odor at its extremities. Also "get a whiff" is by itself another separate idiom within the sentence meaning the same thing. = "to not come close" or "to miss" or "to have no chance" Marlboro is exaggerating the idiom "get a whiff" to Harley by using "Smelly Shit" as the subject of the sentence. NB extra info: "get a whiff" idiom also means not to get even a small percentage of something. "The company went bust last week, but because I had only worked there three months. I never got a whiff of any redundancy pay"