Perhaps some of the jealous monster students who don't want Naruto to succeed in school could be antagonists.
There could be a powerful monster teacher who has a grudge against humans. This teacher could constantly give Naruto a hard time, for example, by grading him unfairly or making him do extra - difficult tasks. The teacher's actions would create a major obstacle for Naruto in his journey at the school for monsters.
It could be a group of traditionalist monsters who believe that humans don't belong in their school. They might try to drive Naruto out by setting up difficult situations for him, like making false accusations or trying to get him to break the school rules. These antagonists would add conflict to the story as Naruto tries to prove himself worthy of being at the school.
In a world where Naruto is a fish out of water, the local bullies or those who uphold the unfair traditions of the world could be the antagonists. They might oppose Naruto when he tries to change things for the better.
Well, it could be that Naruto has to learn how to interact with monster classmates. Maybe he discovers new jutsus that are unique to the monster world in school.
The main antagonists could be the original Naruto's friends and allies. Since this is an evil Naruto, people like Sasuke, Sakura, and Kakashi would likely oppose him and try to stop him from whatever evil plans he has in the past.
The main antagonists could be some of the traditional ninja clans who see Naruto's connection to the monsters as a threat to their power structure. They might fear that the monsters will disrupt the balance of power in the ninja world.
It could be an evil version of Sasuke. In the original story, Sasuke had his dark moments, and in a very dark fanfic, he could be fully consumed by evil and oppose Naruto in a much more malevolent way.
It could be some powerful demon lords in hell. They might see Naruto as an intruder and try to stop him from whatever his goal is.
One possible main antagonist could be the headmaster of the killer school. If the school is a place that values strength and ruthlessness, the headmaster might be a tyrant who enjoys seeing students struggle and fail. He or she could be constantly setting up dangerous situations for Harry just to test him.
Perhaps some students who are jealous of Harry's fame could be antagonists. They might try to undermine him during training exercises.
A jealous classmate could be a main antagonist. This person might be envious of Naruto's popularity and his ability to make friends easily. They could try to spread rumors or sabotage Naruto's projects.
The Akatsuki could still be a major antagonist. Even if Naruto is emperor, they might oppose his rule as it goes against their own goals of chaos and obtaining the tailed beasts.