It could be a demigod who was once shunned and now wants revenge. This demigod has turned to the dark side and uses their powers in a twisted way to cause chaos among the other demigods. They might target the forgotten demigod specifically because they see them as a symbol of all that is wrong with how demigods are treated.
Maybe a group of rogue monsters who have banded together and are led by a powerful and intelligent monster. They target the forgotten demigod because they sense that the demigod has some unique power or knowledge that could be a threat to their plans. The monsters start attacking demigod camps and causing mayhem, and it's up to the forgotten demigod to lead the fight against them.
The main villain could be an ancient Titan who was imprisoned long ago but has now found a way to break free. This Titan could be seeking revenge on the gods and demigods alike, and Percy and his friends would have to stop him before he destroys the world as they know it.
It could be a corrupted demigod who has turned against his own kind. Maybe he was jealous of Percy's status as the hero and decided to use dark magic to become powerful enough to challenge him.
Kronos could make a comeback. Even though he was defeated before, he could find a way to return in a more powerful and vengeful form. He could be the mastermind behind the apocalypse, seeking to finally destroy the gods and take over the world once and for all.
Maybe a group of rogue nymphs who are angry at how the demigods have been treating the natural world. They trap Percy as a warning to the other demigods, and he has to negotiate with them and find a way to make amends for the actions of his kind.
Maybe a new type of monster that is created or awakened during the eclipse. This monster could be immune to most of the demigods' powers during the eclipse, making it a very difficult foe. It could have the ability to manipulate shadows, which are stronger during the eclipse, and use them to its advantage in battles against Percy and his friends.
Perhaps a minor god who is jealous of the attention the major gods get. This god decides to cause trouble at the zoo. He could be the one responsible for making the magical creatures in the zoo act up. He would try to stop Percy from uncovering his plans and restoring order at the zoo. He might have some strange powers related to the natural elements found in a zoo, like the ability to make plants grow wildly to entangle Percy or make the water in the ponds turn into quicksand - like substances.
It could be Kronos again, but in a more powerful and resurrected form. He might have found a way to come back even stronger after his previous defeat and now has a new plan to take over the world of gods and demigods.
Maybe a group of rogue demigods who have decided to take over the Hollow for their own purposes. They could be using the resources of the Hollow in a wrong way, like trying to extract its magic to make themselves more powerful. They would be a formidable foe as they have demigod abilities.
The main antagonist could be an ancient demigod who was forgotten by history but has now awakened. This demigod could be bitter about being forgotten and decides to take revenge on the current demigod world. He might have some dark and powerful magic that he's been developing during his long slumber.
It could be a demigod who was overshadowed by the more well - known ones like Percy. Maybe someone who was born to a minor god or goddess and got lost in the shuffle. For example, a demigod of a nature god who was always in the background while the big battles were fought by the children of the more prominent Olympians.