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.
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.
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.
The Giants might also be antagonists. They could band together and target Percy's kingdom, believing that by destroying him and his rule, they can undermine the power of the gods further. They might use their brute strength and strategic thinking to attack Percy from different fronts.
Another option could be a group of rogue demigods who have turned to the dark side. They follow Percy to Forks, hoping to find some powerful artifacts there. They don't care about the vampires or werewolves and are willing to cause destruction to get what they want. Percy has to stop them while also dealing with the local supernatural creatures.
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.
The Titans could be the main antagonists. Even though they have been defeated before, some of them might have found a way to return or their followers could be causing trouble. They see Artemis as a threat or a target for their revenge against the gods. Another possibility is a new group of powerful monsters that have banded together and are specifically targeting Artemis for her power and influence among the demigods.
Well, the main antagonists could be a group of rogue demigods who have formed a cult around Kronos. They believe that Percy, as the heir of Kronos, should lead them in overthrowing the current order of the demigod world. But Percy doesn't want any part of it, so they become his enemies. Another possible antagonist could be an ancient being that was once in league with Kronos and now sees Percy as a means to resurrect Kronos or continue his dark legacy. This being would stop at nothing to force Percy to embrace his role as the heir.