A jealous courtier could be an antagonist. Maybe someone in the princess's own court who is envious of her position and tries to stop her time - travel adventures out of spite or to gain power for themselves.
Danzo could be a potential antagonist. Even in the past, he might be plotting against the Uchiha clan. If Sasuke and Hinata try to change things related to the Uchiha, Danzo could see them as a threat and try to stop them.
One potential antagonist could be Orochimaru. If Naruto and Temari travel back to a time when Orochimaru was at the height of his power and evil plans, he would surely oppose them. He might see their knowledge of the future as a threat to his schemes to gain immortality and power over the ninja world.
The dark mages of that time could be antagonists. They might sense Shirou's different magical energy and try to either control him or destroy him. Also, there could be traitors within Arthoria's court who don't like the idea of an outsider like Shirou being around and causing changes, so they work against him.
The society at large could be an antagonist. If the woman is seen as villainous because she goes against the norms and values of society, then society as a whole is opposing her pursuit of justice.
Jealous characters could be antagonists. Maybe there are other girls who are envious of the beloved and pampered girl and try to bring her down. Another possibility is that her over - protective family members, in a sense, could act as antagonists if their pampering restricts her freedom too much.
One possible main antagonist could be a dark wizard from the past who senses Hermione's interference in the timeline and tries to stop her. This wizard might be afraid that Hermione's actions will change history in a way that will end his power or influence.
One potential antagonist could be a rogue ninja from another dimension who wants to use Naruto and Naruko's abilities for his own gain. He might be jealous of their power and try to trap them in different dimensions to study their techniques. Another could be a powerful entity that controls the portals between dimensions and doesn't want Naruto and Naruko messing around with the balance of different worlds.
A rival law firm could be the antagonists. They might try to steal Joe's clients or undermine his cases in unethical ways, like spreading false rumors about his legal abilities.
A group of rogue ninjas who have made the island their base could be antagonists. They might see Naruto as a threat to their operations on the island.
A powerful wizard who wants to use the 'lady of darkness' powers for his own evil gains could be an antagonist. He might try to manipulate her into doing his bidding.