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.
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.
A new, original villain could also be the main antagonist. This villain could be someone from Percy's past who has a grudge against him and wants to use the Avengers as a way to get revenge. By making Percy betray the Avengers, this villain can not only harm Percy but also cause chaos among the powerful superhero group.
One possible plot could be that Percy Jackson, in a crossover world, is somehow made to believe that the Twilight characters are a threat to his world. Maybe he's deceived by some dark force into thinking they're planning to take over Camp Half - Blood. So he betrays them by leading an attack on their territory in Forks, not realizing he's been tricked.
It could be the gods. They often have their own agendas and might see the son of chaos as a threat to their power. So they might manipulate Percy into betraying the son of chaos.
It could be a jealous rival. This rival might have always been envious of Percy's popularity and skills. So, they manipulate Percy's friends into betraying him to get Percy out of the way and take over his position.
It could be an ancient evil god who manipulates Percy into betraying the son of chaos. This god might have a long - standing grudge against the son of chaos or his lineage and sees Percy as a useful pawn.
It could be a power - hungry Atlantean noble who wants to rule not just Atlantis but also the surface world. He sees Percy as a threat to his plans and tries to stop him at every turn.
A new and powerful demon that has emerged from the darkest corners of the underworld. This demon is bent on using Percy's connection to the overworld to break through the barriers between the two worlds and unleash chaos. It has powers that are different from what Percy has faced before, like the ability to manipulate the very essence of the underworld's environment.
A powerful Amazonian sorceress who has turned against her own kind and is now trying to use dark magic to take over the world. She could see Percy as an obstacle in her path and constantly try to defeat him.