The Titans could be great antagonists. They have a long - standing grudge against the gods and would see the Percy Jackson Special Forces as a threat to their plans of overthrowing the Olympians. Kronos, in particular, is a powerful and devious enemy.
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.
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.
A likely main antagonist could be a powerful demigod who has turned to the dark side and wants to use chaos for his own evil purposes. He might see Percy as a threat to his plans.
In some fanfictions, it could be an ancient and powerful Titan that has been resurrected. This Titan might be seeking revenge on the demigods, especially Percy and Annabeth, because of their past victories over the Titans. Their powers and knowledge from the old times would pose a great threat to our heroes.
The main antagonists could be the Titans. They are powerful enemies in the Percy Jackson universe already. Now that Percy has Superman - like powers, they might see him as an even greater threat to their plans of overthrowing the gods. So, they would do everything in their power to stop him.
The main antagonists could be the remaining Titans who see Percy as the last obstacle in their plan to take over the world. Since Spartans were known for their great fighting skills, the Titans would want to eliminate Percy to ensure their victory.
The Titans could still be a major threat. Since Percy is now the Host of Chaos, they might see him as a new opportunity to regain power. Kronos could try to manipulate Percy's chaotic powers for his own gain, or maybe use Percy's new status to cause more chaos in the world and then step in to 'restore order' in a way that benefits the Titans.
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 great antagonists. They might see Percy as a threat to their plans of regaining power. Since he has the power of Aether, they could fear that he'll be able to stop them in ways other demigods can't. Another option could be some dark demigods who are jealous of Percy's connection to Aether and want to steal his powers for themselves.
Obviously, the Primordial of Destruction itself would be a major antagonist. It's a powerful and chaotic force that wants to bring about destruction. But also, there could be some demigods who are influenced by the Primordial's power and turn against Percy. They might be jealous of his power or simply be corrupted by the allure of destruction. Another possible antagonist could be an ancient cult that worships the Primordial of Destruction and is trying to bring it back to full power. They would do anything to stop Percy from interfering with their plans.