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Ok, lets say everyone here finds themselves on, Mars. Achilles and Leonidas are unaffected by the gravitational variables. However, Johm Carter gains all of the physical abilities he displayed capable of doing in the film.

The fight would take place in a large desolate area of, Mars with many many steep mountain sides flat open areas.
John has two swords and a dagger with light armor. Achilles is outfitted in light armor with a heavy circular shield as well as a javelin and a short sword. Leonidas in light armor wields a heavy reinforced shield, and short sword and a long spear.

....,Who wins?

As John Carter does one of his silly long jumps towards them, both Leonidas and Achilles throw their spears and skewer him.

Did they ever show good enough aim to hit something that small going that fast?

The Spartans had ridiculously good aim. Achilles did too, iirc.

I'm not doubting their aim. I'm asking if they can hit him(a human sized target) at the speed he goes during one of his jumps.

Considering their aim, don't think it's beyond either of them.

Let's also not forget that he had enough agility to evade, then catch a sword thrown at him in mid jump.

All I know is Achilles was very nasty with that spear lol. I always lol when the guy right next to Hector gets pawned before they first met.

John one shots them both.

yeah, I'm thinking John wins this one. The advantages that he has at his disposal could insure an easy victory. John might be to fast and strong for Achilles.