This one might end up being a little bit personal opinion rather than hard fact.
The way I see it, Achilles is the most likely to win here. Because, even though Maximus is a very skilled opponent, he just isn't on the crazy level that Achilles and Perseus are on. And although Perseus(this is where opinion comes in) has his magic sword and shield, those pieces of equipment are only as useful and effective as the user is. And by what I saw, Perseus isn't as good as Achilles when it comes to raw skill. Therefore, you have my verdict.
Tune in next time!