- Which Mythology/Mythologies?
- What Kind of Pirates?
- Where are they?
- Why is the Villain in Conflict with the Hero?
Since they're described as "Mythic Pirates", there's the possibility of having non-human characters, either pure mythic creatures, such as Medusae, Cyclops etc, or perhaps human/mythic hybrids.
The next problem is location - the best answer is probably a fictionalised Mediterranian, with plenty of small islands and citystates, as this will offer plenty of scope for stories (and, from the point of view of making the fictional world work, lots of city-states means lots of trading, which means lots of merchants; the island nature of the city-states means these will be merchant ships; lots of merchant ships means lots of opportunities for pirates; and the abscence of large countries means an absence of large, organised, anti-pirate forces)
As for time period, sticking to the Ancient Greek/Roman period would instantly add novelty, since there would be no gunpowder, hence no cannons. Fortunately, there would still be opportunities for the classic ship-to-ship fighting, since the Ballista was invented by the Ancient Greeks. It might also be an idea to chuck in magic, perhaps for the villain, as this would offer the possibility of flashy effects. The main challenge would be combining traditional "Pirates" (eye patches, tricorn hats etc) with an Ancient Greek aesthetic, although this may turn out not to be necessary, since a Greek aesthetic could provide a fantasy environment.
The best reason for the conflict between hero and villain is probably a MacGuffin; either something they both want, or something the Hero has stolen from the Villain (since the Hero is a pirate, this MacGuffin is probably a treasure of some sort, although it might concievably be the Hero's boat).
The last question is the nature of the Villain - either an active equal (an evil pirate, for example) who they are in direct conflict with, or a passive superior (evil sorceror/sea god) who sends minions to confront the Hero.