I can tell you who DOESN'T win:
Spartacus
Maximus
Ragnar lothbrook
zorro
baseball bat guy from raid 2
They are all human, although each highly skilled, they are after all human.
3 left who should be the odds on favorites to win:
Despite Conan being human, as ABE FROMAN has mentioned, beat non-humans - mighty feats indeed. However, he is still human.
Achilles was a practically a demi-god, son of a nymph and human king. His mom, trying to make him immortal dipped him in the river Styx. His only vulnerability was his heel, hence the term 'achilles heel' to mean a weakness - a chink in the armor so to speak.
The Highlander is immortal. The immortals can only die if beheaded by another immortal. We don't see in the movies/tv if a human tries to behead an immortal (i don't recall).
The question then boils down to if these 3 know each others' weaknesses. Most swordsman will not think of attacking someone's heel. Most of the time they will be standing. Depending on their preferred attacks, the swordsmen may look to slash and thrust the arms/body in favor of going for a beheading.
Leaning towards Achilles, but it really boils down if they knew the weaknesses and specifically go targeting. Achilles may stab Highlander thinking he won, but highlander then decaps Achilles and finds he can't. With Achilles' sword stuck in him, he just continue to attack a weaponless Achilles.