Perhaps Orochimaru from Naruto could be the main antagonist. He's always seeking more power, and in this fanfic, he might see the powers in 'The God of High School' as a means to achieve ultimate power. He could try to manipulate the events of the 'The God of High School' tournaments to his advantage, all while causing chaos in Naruto's world as well.
Perhaps a strict teacher who doesn't like Naruto's unorthodox ways and Anko's rebellious attitude. The teacher might try to split them up and prevent them from participating in school activities together. For example, if they want to enter a school competition as a team, the teacher could create obstacles.
Loki could be a great main antagonist. He could be the mischievous student who's always causing trouble for the Avengers. He might use his magic to play pranks on them or steal their homework to make them look bad in front of the teachers.
It could be a jealous classmate. Maybe someone who has a crush on Armin and sees Annie as a threat to their relationship. This person could try to spread rumors about Annie to make Armin stay away from her.
Perhaps a jealous classmate who discovers Artemis's connection to the fairy world. This classmate wants to use that knowledge to gain power and popularity, so they start causing trouble for Artemis and his friends, trying to expose them to the wrong people or get in the way of their fairy - related investigations.
Gary could be a main antagonist. He might be jealous of Ash's popularity at school and constantly try to undermine him in Pokemon battles and in front of their classmates.
The Organization in the Claymore world could be the main antagonist. They already have a lot of secrets and do some morally ambiguous things. If Naruto shows up and starts changing the status quo, like teaching Claymore warriors to be more independent, the Organization might see him as a threat and try to eliminate him.
It could be a rogue ninja who was once a student of Orochimaru and has now developed his own dangerous jutsu. He wants to take over the ninja world and believes the old ways are holding everyone back.
Orochimaru could be a great antagonist. He might want to use Shenron's power for his own dark experiments. He could try to steal the dragon balls and manipulate the wishes to gain immortality or create an army of powerful, immortal ninja.
It could be someone who opposes Naruto's newfound admiration for Ganondorf. Maybe a traditionalist ninja who thinks Naruto is straying from the true ninja path by getting influenced by Ganondorf.
Lex Luthor could be a great antagonist. He's always looking for power and knowledge. If he discovers Naruto's abilities, he might try to use them for his own gain or see Naruto as a threat to his plans in Smallville.