The Titans could be the main antagonists. They might oppose Percy's ascension to Olympian status because they see it as a threat to their own plans of overthrowing the Olympians.
The Titans might still be a threat. Even though they were defeated before, they could have some remnants or followers who don't want Percy to become an Olympian because it would strengthen the Olympian side even more.
Maybe the gods or powerful beings who are trying to maintain the current balance and see Percy's new role as a disruption. They would try to stop him from carrying out his assassinations in the chaos world.
The Titans could be the main antagonists. They might see Percy becoming a guardian of the Hunt as a threat to their plans. Since the Hunt has its own power and influence, the Titans would want to disrupt it. They could send their minions to attack the Hunt, and Percy would have to use his skills and newfound position to fend them off.
Well, perhaps Percy has to go through a series of trials. He might need to prove his worthiness to the Olympians. Maybe he has to battle some mythical creatures that are threatening the Olympian realm. And in the end, he gains the recognition and powers of an Olympian.
In this fanfiction, it could be that Percy is chosen for a special task by the existing Olympians. They see his potential not just as a hero but as someone who could join their ranks. So he gets trained in Olympian magic and lore, which is very different from what he's used to. He has to learn how to control new powers and also deal with the politics among the Olympians.
It could be an ancient deity that was banished long ago. Maybe a primordial god or goddess who was considered too powerful or too dangerous for the other Olympians. For example, it could be Erebus, the god of darkness.
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.
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.
There could be an old dragon that has been in exile for a long time. This dragon might see Hiccup as a threat to its plan of taking over the dragon kingdom. So it tries to stop Hiccup from fully becoming a dragon or tries to use his new form for its own evil purposes.