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.
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.
Obviously, the Primordial of Monsters itself could be the main antagonist. It has the power and the motive to cause chaos and destruction, which would put it directly in opposition to Percy and his friends.
It could be a new, powerful Titan that has emerged from the depths of Tartarus. This Titan might be jealous of the eldest primordial's power and wants to either destroy it or take its power for itself. And since Percy is associated with the eldest primordial, he becomes the Titan's target as well.
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.
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.