There could also be some ancient monsters or spirits that are tied to Olympus' existence. They might rise up to defend it because their own survival is linked to the continued existence of Olympus. These could be powerful beings that Percy has never faced before, adding an extra layer of danger to his quest to destroy Olympus.
Obviously Percy would be one of the main characters. There might also be other characters from the Percy Jackson series like Annabeth. Maybe the gods of Olympus would also be important characters as they are the ones whose home, Olympus, is being destroyed.
Grover could also be a major character. As Percy's best friend, he would probably be involved in trying to stop Percy if he thinks Percy has gone too far. Or, if he sees the corruption in Olympus, he may side with Percy. Grover's connection to nature means he could play an important role in the events that unfold, like using nature spirits to either protect Olympus or aid Percy depending on his stance.
A new main antagonist could be a forgotten or banished god. There are many minor gods in Greek and Roman mythology that haven't been explored much. One of them could be angry at the demigods for getting all the attention and decide to cause chaos. For example, a god of misfortune who decides to curse the demigods with a series of bad luck that leads to dangerous situations.
The Titans could still be antagonists. In the Percy Jackson universe, they are powerful and malevolent. A princess in a fanfic might have to face their wrath as they try to overthrow the gods and take over the world. They would see the princess as a threat, especially if she is allied with the gods or has some special power that could stop them.
The Olympians themselves could be the main antagonists in a sense. Since Percy is betraying them, they would be the ones trying to stop him. Zeus, with his power and pride, would likely be at the forefront, seeing Percy's betrayal as a direct threat to his authority.
A new and powerful Titan who has been hiding and gathering strength all this time. He could be jealous of the Olympians' power and wants to take over. Percy would have to figure out his weaknesses and stop him before he causes too much destruction.
I'm not entirely sure specifically as it's a fanfic. But generally, it might involve Percy having some extraordinary power or facing a situation that forces him to destroy Olympus. It could also be a really creative take on the existing Percy Jackson universe, where the author wants to explore a different and more radical storyline compared to the original.
The Titans could be great antagonists. They might see Percy as a threat because of his connection to Thanatos and the power it could potentially give him. Also, some rogue underworld creatures, like powerful demons or vengeful spirits, could oppose Percy. They may not want Thanatos to have a more powerful influence through Percy.
Some of the more powerful and vengeful spirits in the Underworld itself could be antagonists. They might not want an outsider like Percy to be the Champion of Hades. They could try to undermine him at every turn, like spreading false rumors about him among the other Underworld denizens or directly attacking him when he's vulnerable during his quests in the Underworld.
Some of the primordial gods who are jealous of Chaos's newfound relationship with Percy could be antagonists. They might view Percy as an upstart and try to undermine his position. For example, Erebus could try to create chaos in Percy's life in a more malicious way, not in the way that Chaos intends.