The main antagonist could be Hades in a time loop fanfiction. Hades might be angry that Percy keeps interfering in his plans in the Underworld. So, he uses his power over time in a limited way to create a time loop for Percy. In the loop, Hades sends various underworld creatures to harass Percy, and Percy has to find a way to break the loop and make peace with Hades to stop the cycle.
A really interesting antagonist for a Percy Jackson time loop fanfiction could be a new character, perhaps a powerful magician who is jealous of Percy's powers and status. This magician creates the time loop to drive Percy insane. He constantly manipulates the events within the loop, making it seem like Percy's friends are turning against him. He does this all while hiding in the shadows, making it difficult for Percy to figure out who is really behind his time - trapped misery.
It could be Kronos. Maybe he's found a way to trap Percy in a time loop as part of his plan to stop Percy from fulfilling his destiny. Each time Percy breaks free from the loop a little, Kronos throws new challenges at him.
Maybe a corrupted past version of a demigod. For example, a demigod who was promised great power by the Titans and turned against the Olympians. This demigod could see Percy as an obstacle to their plans and try to stop him at every turn. They would know the time period well and could use that to their advantage against Percy.
Another antagonist could be a primordial from another realm who is jealous of the power of the primordial of time. This primordial decides to invade the 'Percy Jackson' world and try to absorb the power of the primordial of time. It would bring a whole new level of threat as it has its own set of powers and minions from its own realm. It could also be that this primordial has the ability to twist time in its own realm, and when it enters the 'Percy Jackson' world, it starts causing chaos with time there as well.
It could be an ancient being that was locked away for centuries but has now been released due to Percy's meddling with time and tides. This being might have a vendetta against the gods in general and sees Percy as a key to achieving its revenge. It could have the power to manipulate time in a different way than Percy, causing all sorts of chaos and destruction. For example, it could create time loops that trap people in never - ending cycles of pain and suffering, and Percy has to figure out how to break these loops and stop the being.
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.
Maybe it could be a demigod who has become obsessed with power through gaming. This demigod, let's say a child of Hades, discovers a way to use dark magic and combine it with gaming technology to try and rule over all the other demigods. He sees Percy as a major threat to his plans because Percy is so popular and has strong powers, so he constantly tries to undermine Percy at every turn.
The goddess Hera might also be a great antagonist. Since she has a history of interfering in the lives of demigods, she could be jealous or threatened by Percy's rebirth. She might try to stop him from reaching his full potential in his new life or cause trouble between him and his new allies.
A powerful demigod who has been corrupted by the idea of primordial power could be the main antagonist. They might believe that by allying with a primordial or obtaining their power, they can become greater than the gods. This demigod would then oppose Percy, who stands for the protection of the current order.
An ancient and forgotten god who has been awakened. This god could be angry at the modern demigods for ignoring the old ways and decides to send assassins after Percy as a warning to the rest. They might want to bring back the old order where gods were feared and worshiped more and see Percy as a symbol of the new, more independent demigods.