The main antagonists could be the Titans. They are powerful enemies in the Percy Jackson universe already. Now that Percy has Superman - like powers, they might see him as an even greater threat to their plans of overthrowing the gods. So, they would do everything in their power to stop him.
In this type of fanfiction, Darkseid could be a major antagonist. He is one of Superman's greatest foes. If he discovers that there is a 'son of Superman' in the world of Percy Jackson, he might try to invade that world to either capture Percy or use the power of the demigods for his own evil purposes. Also, some of the traditional demigod villains like Ares might also oppose Percy more strongly now. They might be jealous of his new powers and see him as a threat to their status among the demigods.
Perhaps Hades could be an antagonist in this fanfiction. He is often at odds with Percy in the original Percy Jackson stories. Now with Percy having Superman - like powers, Hades might feel that Percy is getting too powerful and could potentially disrupt the balance in the underworld. Also, the villains from Superman's world like Metallo could be brought into this story. Metallo, with his kryptonite - based powers, could pose a serious threat to Percy if he manages to find a way to counter Percy's demigod and Superman - like abilities.
A practical answer is Chapter 265, because it turns the idea into a concrete scene. The chapter opens with As expected, the truth behind the video was unearthed one by one and..., adds pressure through Although his accomplices have also shared some information, there's still..., and ends on Miss.
Chapter 266 is the strongest chapter-level answer because it starts from Upon hearing this, the deputy director's expression also turned serious. and follows through on Now I see why Jiang Li despises her brother so much, utterly unreliable!"....
Chapter 298 is the strongest chapter-level answer because it starts from Grandfather, I, I can testify, everything Sister said is true." Right as... and follows through on I've just recovered from being sick, I've just returned to the Capital,....
The best chapter pointer here is Chapter 225, "Just 100,000? Are you buying mineral water for the boss?". It opens with When Zhao Lang's devastatingly handsome face appeared, all six people... and closes on Which big shot is inspecting again???] [The ID is still in the United Arab....
Look to Chapter 280 for the clearest answer. It begins with The small mountain village was already dark and lightless at night, and..., keeps building through Zhao Lang didn't dare to waste time;
A practical answer is Chapter 264, because it turns the idea into a concrete scene. The chapter opens with Jiang Li first reassured her mother, then opened the chat box with Shen..., adds pressure through The resulting clarity from this information coming to light was far more..., and ends on [Do.
Chapter 271 is the strongest chapter-level answer because it starts from He had barely finished speaking when he received a withering look from... and follows through on Gathering her thoughts, Jiang Li looked toward Jiang Yan, who was still....
Chapter 268 is the strongest chapter-level answer because it starts from To ensure the company's successful listing, Shen Lan even went so far as... and follows through on Jiang Li has nothing to do with Director Sun!" "Because she is my niece!"....
The best chapter pointer here is Chapter 279, "The Sudden Blaze". It opens with After getting a good scolding, Jiang Yan resigned himself to lying quietly... and closes on I can't take it anymore," Jiang Yan exclaimed with a weak breath, the....
Chapter 230 is the strongest chapter-level answer because it starts from Shang Shaojing's expression wasn't looking too good either. and follows through on If he knew that your stepmother was secretly prompting you towards a.... The payoff is that the chapter closes with "Liu Linmei!