It could be a jealous demigod. Maybe someone who has always been in Percy's shadow and decides to frame him for betraying the gods in order to get rid of him and gain more power and recognition among the demigod community.
The main antagonist might be an ancient, powerful being that has a vendetta against the gods. This being manipulates Percy into actions that seem like a betrayal of the gods. For instance, it could be a Titan who has been biding its time and sees Percy as a useful tool to disrupt the current order of the gods.
There's a possibility that the main antagonist is a corrupted god. A god who has become power - hungry and wants to get rid of Percy because he is seen as a threat. This god spreads false rumors and sets up situations that make it look like Percy has betrayed the others, all in an attempt to protect their own status and power within the divine realm.
It could be Ares. He might see the Twilight vampires as a new source of power or chaos. He manipulates Percy into believing that the Twilight characters are evil and need to be stopped. So Ares becomes the main antagonist as he's the one driving Percy to betray the Twilight group.
It could be a rogue member of the Hunt. Maybe someone who has a personal vendetta against Percy for some past event or just out of jealousy. This character might be secretly plotting against Percy within the Hunt and is the one who orchestrates the betrayal.
Apollo might be the betrayed god. He could have been tricked by another god into betraying Percy. For example, Apollo might have been promised more power or a higher status among the gods if he turned against Percy. But then he realizes too late that he's been used and that he's actually betrayed someone who could have been an ally.
One possible main antagonist could be Cronus, an Elder God. He has a history of trying to overthrow the Olympians and could be plotting a comeback in the fanfiction. He could be using his powers to corrupt demigods and turn them against each other, all in an effort to regain his former glory and power over the world.
Maybe it could be a group of dark sorcerers. They are jealous of Percy's newfound powers as the God of the Sun and they want to use his power for their own evil purposes. They try to trap Percy and steal his powers by using dark magic and illusions.
It could be a new and unknown deity who is jealous of Percy's sudden ascension to the status of God of Elements. This deity might be able to manipulate the dark aspects of the elements and use them to create havoc and try to defeat Percy. For example, the deity could create poisonous miasmas using the water element or uncontrollable infernos with the fire element. He would constantly be one step ahead of Percy, making him a very difficult antagonist to deal with.
It could be an ancient and powerful Titan who was once in charge of fate but was overthrown. Now he wants to regain his power over fate and sees Percy as a threat. He might try to manipulate Percy into making bad decisions regarding fate.
Perhaps a powerful sorcerer who has somehow managed to gain control over some of the angelic powers and wants to use them to rule the world of demigods. He could be jealous of Percy's connection to the angel of God and see him as a threat to his plans. This sorcerer would use dark magic combined with the misused angelic powers to create all kinds of obstacles for Percy and his friends.
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.
It could be a new, dark demigod who has been corrupted by dark magic. This demigod might envy Percy's relationship with the gods and the God of Thunder in particular. He or she could be gathering an army of monsters and using dark powers to try and take over the world of the demigods and gods alike. They would be a formidable foe as they understand the ways of demigods but also have access to dark powers that are not easily countered.