It could be a rogue demigod who was on the losing side of the Giant War and is now seeking revenge. This demigod might have found some dark power or be allied with some minor but dangerous mythical creatures.
Perhaps the main antagonist could be an ancient god or goddess who was displeased with how the Giant War ended. They might see the demigods as a threat now that they've proven their strength and decide to take matters into their own hands to restore the old order. For example, a minor god who has been forgotten but now wants to regain power by eliminating the demigods.
In a 'Percy Jackson after Giant War' fanfiction, the main antagonist could be a group of mortals who have learned about the demigods during the war. They form a secret society and use their knowledge of technology and modern warfare to try and hunt down the demigods. They see the demigods as a danger to the mortal world and want to wipe them out, creating a new kind of conflict for Percy and his friends.
In the fanfiction, Percy might face new challenges related to his demigod status. Maybe he has to deal with the aftermath of the war, like rebuilding Camp Half - Blood or helping new demigods adjust.
Perhaps the antagonist could be a corrupted demigod. Someone who was also in Tartarus, but instead of coming out stronger in spirit like Percy, they were twisted by the darkness there. They now want to bring that same darkness to the world of the demigods and see Percy as the main obstacle to their plans.
One possible plot could be Percy and his friends dealing with the aftermath of the war in the mortal world. Maybe they have to hide their demigod identities even more carefully as the war has drawn some unwanted attention. They could also be working on rebuilding Camp Half - Blood and trying to make it safer for new demigods.
There could be new demigods. Maybe some who were hidden during the giant war and now come out. For example, a demigod of a less - known god or goddess.
Another possibility is a demigod who has turned against the other demigods and sided with a particularly cruel god. This demigod could have been corrupted by power or a desire for revenge, and they use their knowledge of the demigod world to help the god in the war. Percy would then have to face this former ally, which would be a very emotional and difficult conflict for him.
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.