Maybe there are some dark forces at work. They sense Percy's growing power and want to stop him before he becomes too strong. These could be ancient evils that have been awakened by Percy's power development. They could send minions or create illusions to make Percy's training difficult.
There could be a group within the camp who don't believe Percy should be training his powers in a certain way. They think he's being too reckless or that his training might endanger the others. So, they act as antagonists by trying to halt his training, even though they might not be truly 'evil' in the traditional sense.
It could be some of the other trainees who are jealous of Percy's progress and his special relationship with Chaos.
One possibility is that Percy trains his powers with the help of his friends. They could create special scenarios or obstacles for him to overcome, which in turn helps him to develop his powers further. His powers could also start to evolve in unexpected ways during this training process.
The Akatsuki could be antagonists. They might see Sakura being trained by Madara as a threat to their plans. Since Madara has his own motives and is associated with the Akatsuki, they could fear that Sakura will become a powerful force against them if she is fully trained by him.
Well, in most fanfictions where Percy trains in Tartarus, it often involves him facing extreme challenges. He might be learning to control new powers or just surviving the harsh environment. For example, he could be training to fight stronger monsters that lurk in Tartarus.
It could be the traditional villains from the original story, like the Titans or some powerful monsters. They might torture Percy to get information or just to cause chaos.
It could be an old enemy from Greek mythology that has been resurrected. For example, a powerful Titan who has a vendetta against the demigods, especially Percy and Annabeth.
Obviously, Percy would be one of the main characters. Since it's about him training in Tartarus. And Annabeth might also be involved. Maybe she's helping him in some way, or she's waiting for him outside Tartarus while he trains.
Perhaps the fanfiction could be about Naruto training Percy in stealth. Percy, being a demigod, often charges into battle head - on. Naruto, on the other hand, is a master of stealth. He could teach Percy how to move quietly and undetected. This would be a great advantage for Percy when he has to infiltrate a monster's lair or spy on the enemy. The story could show Percy struggling at first but gradually getting better with Naruto's guidance.
Well, perhaps Percy could be learning some new and powerful combat skills from Chaos. Maybe Chaos teaches him to manipulate chaos energy in unique ways for battle.
The Underworld could also be a setting. He might be training there to face the dark forces. The dangerous environment full of monsters and traps would provide him with ample challenges to improve his combat and survival skills.