The Giants could also serve as antagonists. They are known for their strength and hatred towards the gods. The son of Hades, being related to the underworld, might be a target for them. They could try to capture him to use his powers to open portals to the underworld for their own evil purposes.
Another option could be some rogue demigods who are jealous of the son of Hades' powers. They might form a group and try to cause trouble for him and Percy Jackson. They could be working with some minor gods who have a grudge against Hades, creating a complex web of enemies.
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 more malevolent spirits or monsters from the Underworld could also be antagonists. They might resent Percy for being Hades' adopted son and try to undermine him. For example, a powerful undead general who believes he should be the one favored by Hades instead of Percy.
The main antagonist could also be an ancient and powerful spirit from the underworld that was sealed away long ago. Percy's presence as the son of Hades accidentally awakens this spirit. The spirit then starts to spread darkness and despair throughout the world of the demigods, and Percy has to find a way to stop it before it's too late.
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.
The Titans could be the main antagonists. Even though they were defeated before, they might see Percy as a threat because of his powerful parentage. They could try to stop him from fulfilling a prophecy or gaining more power. For example, Kronos might have some remaining influence and try to manipulate events to destroy Percy.
Gaea herself would obviously be a main antagonist. She has the power to manipulate the earth and all its forces against Percy. Her children who are fully committed to her cause could also be major antagonists. They might have powers related to the earth and be very difficult for Percy to defeat.
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 Titans could be great antagonists. Since they once rebelled against the gods, they might see Percy, as the son of Selene, as a threat to their plans of regaining power. They could try to capture him to use his connection to Selene for their own dark purposes. For example, Kronos might want to use Percy's powers to control the moon and disrupt the balance of the world further.
The Titans who don't want Rhea to gain more power through Percy could be antagonists. Kronos, for example, might see Percy as a threat to his own plans for domination.
Another option could be some power - hungry demigods. They might not like the idea of Percy, as the son of Themis, having the potential to bring real justice to the demigod world. They could try to undermine him at every turn, creating all sorts of obstacles for him in his quests.