It could be a powerful demigod who has been corrupted by the God of Demons' power. This demigod might have his own agenda and wants to use the chaos caused by the God of Demons to take over the demigod world.
Another possibility is a vengeful minor god who feels that Percy and the other demigods have overstepped their bounds. This god might team up with the God of Demons, not really caring about the demon god's goals but just wanting to get back at Percy and his friends. The minor god could bring in some unique powers and challenges that Percy has to overcome.
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.
A powerful Titan who was once in charge of storms and wants his power back. He sees Percy as a threat and tries to stop him at every turn.
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.
It could be a dark demigod who is also seeking the power of the first god but for evil purposes. This demigod might be jealous of Percy's connection to the first god and tries to stop him at every turn.
Orochimaru might also be a main antagonist. He is always after power and knowledge. In the context of the 4th war with a god involved, he could see the god as a source of ultimate power. So he might try to manipulate the situation to either steal the god's power or use Naruto to get to the god's power. He could be secretly working behind the scenes, causing trouble for Naruto and his allies.
The main antagonist could be a cult that worships the dark god of lust. They might be trying to bring about the full power of the dark god by using Percy as a sacrifice or a vessel. They would be constantly opposing Percy and his friends, trying to stop them from thwarting their evil plans.