A corrupted demigod could be the main villain. During an eclipse, they are influenced by some dark magic and turn against their own kind. They know all the demigods' weaknesses and use that knowledge to cause chaos. They might even team up with some minor gods who are also disgruntled with the current order of things in the Percy Jackson world.
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.
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.
A powerful dark wizard or sorcerer from a different realm could be the main antagonist. The eclipse could have opened a portal to their realm, and they see the world of Percy Jackson as a new place to conquer. They would use their dark magic against Percy and his friends, and Percy, as the God of Eclipse, would have to use his unique powers to stop them.
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.
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.
It could be a new demigod who has a grudge against the Olympians. This demigod might be using Percy as a tool to carry out their assassination plans.
A mythological creature that has infiltrated the government agency could be the main villain. For example, a shapeshifting monster that has been causing chaos within the agency and trying to undermine its operations. Percy would have to figure out its true identity and stop it. Another option is a rogue demigod who has turned against his own kind and is working with the wrong side of the government to cause trouble for Percy and his friends.
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.