Hercules is also invulnerable as long as he's wearing the lion pelt, which I believe he would. Also, his strength eclipses Achilles to the point of hilarity and he'd have no trouble manhandling him.
I agree with Neme. He drops a huge rock on him or tosses him a few miles away into the ocean or something.
To be fair I always wondered about this just cause I always thought Achilles was awesome but I too feel Herc would take this, heck even if it was DC Achilles vs Marvel Herc I'd say Herc takes it...but that Achilles is pretty graceful so...NO BIAS ASIDE, Herc comes out on top (I'm stretching my bias a bit, I like Hercules just as much lol.)
OH WHAT ABOUT THAY GUY JASON FROM ummm uhh...Rise of the Argonauts? Or was he just a human? That's actually one of the tales I'm not too familiar with, the Argonauts, I just played the game (Actually played it the whole way through, had some bugs but I liked it more than most people it seems. Kinda reminded me of Mass Effect but in Ancient Greece xD). Cause if he's only human then..scrap that idea about him vs Herc lol.