It could be the navy. They see pirates as outlaws and would be determined to capture Percy and his crew. They might have better - equipped ships and more trained soldiers, making them a formidable foe for Percy and his fellow pirates.
There could also be some mythical creatures acting as antagonists. For example, a sea serpent that guards a certain passage or a mermaid who lures sailors to their doom. Percy would have to figure out how to either avoid or defeat these creatures while trying to carry out his pirate activities.
The main antagonists could be other pirate crews. There might be a particularly ruthless pirate captain who wants to take over Percy and Annabeth's ship and all the treasures they might be after. This captain could be jealous of Percy's powers and see him as a threat.
One potential main antagonist could be a powerful pirate captain who sees Harry as a threat to his control over the seas. Maybe this captain has some dark magic powers as well.
The traditional wizarding authorities could be antagonists. Since Fem Harry Potter is into pirate stuff which might be seen as unorthodox in the wizarding world, they could try to stop her from following this new path.
Monsters could also be antagonists. With Percy in a new, more powerful state as a godling, there could be new and more powerful monsters that are drawn to his power. These monsters might be stronger and more intelligent than the ones he faced as a demigod, and they could be after his godly essence or trying to use him for their own dark purposes.
A powerful sorcerer who wants to use Percy for his own dark purposes could be an antagonist. This sorcerer might see Percy's unique abilities as a key to unlocking some sort of forbidden magic.
Maybe an ancient sea demon that has possessed a pirate captain. This possessed captain is now leading his crew to cause chaos everywhere. They are attacking other pirate ships and even some demigod - related places. Percy has to find a way to exorcise the demon from the captain and stop the crew's rampage. The demon is very cunning and uses the pirate's knowledge of the sea to its advantage.
The other gods who are jealous of Percy's new connection with Hades could be antagonists. For example, Zeus might see Percy as a threat now that he has Hades' blessing.
The old - fashioned and conservative gods who don't like the idea of a new, young god like Percy shaking up their established order could be antagonists. They might see him as a threat to their power and try to undermine him.
In this kind of fanfiction, the Titans could also be antagonists. They might want to use Percy's power over time to their advantage. Maybe they think they can rewrite history in a way that would bring them back to power. Kronos, in particular, if he were somehow still a threat, could be a major adversary. He could try to manipulate Percy into using his time powers in a way that would benefit the Titans, like going back and changing events that led to their downfall.
The main antagonists could be some of the more traditional and power - hungry gods. For example, Hera might see Percy as a threat to the order she has maintained for so long. She could try to undermine him at every turn, fearing that his new ideas and his relation to Zeus will disrupt her plans. Another antagonist could be Ares, who might be jealous of Percy's potential power and influence over the other gods and demigods.