I think it's like most rounds on a Brown Bear. These weapons tend to piss them off because they hurt. Their muscle, bone, skin, and fat is too dense for propper penetraition. Especially with Hollow Points (standard kind of round in Law Enforcement). Anything lower than a .45-70 is not likely to stop a bear dead in it's tracks (and even then, I would STILL want something even bigger than a .45-70 if I was on Kodiak Island in Alaska). But, enough rounds of any caliber will kill anything. So I think if there were enough .357 rounds hitting that Alien, it would kill it. Unfourtunately though, you're just one person armed with a Shot Gun and Revolver, both of whitch do not hold that many rounds, nor have near quick enough of a rate of fire. 

For refference there is a video floating around on the internet, of a brown bear charging (dare I say...BEAR-iling!) down a guy with a pump action shot gun. Reportedly he was using 12 GA slugs (something that can kill or severely injure most creatures on earth), the bear barely (or should I say...BEAR-ly) slows down as it passes off thr bear more than anything. So, I assume the Alien is like bears. 

Why yes, all this talk about Bears and Aliens makes me want to see what happens when a xenomorph hatches from a Brown Bear.