Maybe even a minor god or goddess could be his mentor. For instance, the goddess of magic, Hecate. Since shapeshifting has elements of magic, she could teach Percy the more mystical aspects of his new power. She could show him how to use shapeshifting not just as a physical transformation but also as a way to manipulate his essence in the magical realm.
Annabeth could also be a sort of mentor. She's very intelligent and could research about shapeshifting in the ancient texts. She could help Percy figure out how to control his ability better by coming up with strategies based on what she's learned from the books. For example, she might find a way to help Percy focus his mind to prevent unwanted shape changes.
Another option could be a mortal martial arts master who unknowingly stumbles upon Percy. The mortal is a master of a rare and ancient form of martial arts. At first, he is hesitant to teach Percy because he senses something different about him. But as he gets to know Percy better, he realizes Percy's good heart and decides to train him. This would add an interesting dynamic as Percy has to balance his demigod life with his training under a mortal.
Perhaps the Sage of Six Paths could be his mentor. Since the Sage has great knowledge and power, he could guide Naruto in understanding and using soul magic. Another option could be Jiraiya. Even in death, Jiraiya's spirit could communicate with Naruto and teach him about soul magic through visions or dreams.
It could be an old hermit living in the forest who has a deep connection with nature and Mokuton. This hermit has been observing Naruto from afar and decides to come forward to teach him. The hermit could have a different approach to using Mokuton, one that is more in tune with nature's balance, which Naruto would find both challenging and enlightening.
Another option could be Black Widow. She's very good at adapting to new situations and using her skills in different ways. For Percy, who is coming from a very different world, she could teach him how to be stealthy and use his powers in a more covert way. She could also help him with understanding the political side of the Avengers, like dealing with government agencies and such, which Percy may not be used to in his world of demigods.
She could be the daughter of a minor god that hasn't been introduced much in the original Percy Jackson series. For instance, the daughter of Hecate. This would give her powers related to magic, which would be really cool in the context of the story. She could use her magic to help Percy and his friends in battles or to solve some of the mysteries they encounter.
Perhaps she's a sister who was thought to be dead but actually survived. She could have been corrupted by the experiences she had while being 'dead'. When she returns, she blames Percy for not saving her properly. This false blame leads her to betray Percy. She could start spreading rumors about Percy being a coward or a bad leader among the demigod community.
Eragon could be one of Percy's allies. Eragon has his own set of powers and knowledge of Alagaesia. Percy and Eragon could combine their skills, with Percy's control over water and Eragon's magic and sword - fighting abilities. They could also share their different cultural knowledge, Percy from the world of Greek mythology and Eragon from the world of Alagaesia.
There could be a demigod who is the child of a minor god that we haven't seen much in the original series. For example, the child of Hebe, the goddess of youth. This character could bring a fresh perspective with their powers related to rejuvenation and vitality.
The spirits of the maze itself could turn against Percy. They could be angry at all the demigods who have been trespassing for years and decide to stop Percy from getting through by any means necessary.
In his new life, Percy could meet a kind - hearted librarian. She would be the one to introduce Percy to a whole new world of books that he never had time to explore before. There's also a chance that he'll meet a street - smart kid who helps Percy navigate the more mundane aspects of his new life, like finding the best places to eat or how to fix his bike. And perhaps a new teacher who has a mysterious past and seems to have an inkling of Percy's true nature.