It could be a group of rogue ninjas who also ended up on the island. They might be after some valuable resource on the island and see Naruto and Tsunade as obstacles.
In some 'naruto and tsunade island fanfiction', the main antagonist could be a power - hungry warlord who has made the island his base. He wants to capture Naruto for his unique abilities and Tsunade for her knowledge and power. So he sends his minions after them, and he himself might be a very powerful opponent with his own set of deadly jutsus.
It could be a group of rogue ninjas who want to steal Naruto's godlike powers for themselves. They might be led by a powerful and evil ninja who has his own motives for wanting such power.
Often, it could be the same antagonists from the original Naruto series but in a different context. For example, Orochimaru might still be an antagonist if he tries to use the time - travel situation to his advantage, like getting his hands on some ancient forbidden jutsu.
Often, Orochimaru can be a main antagonist. Since he has his own devious plans in the Naruto universe, in a time - travel scenario, he might oppose Naruto and Tsunade's attempts to change things for the better. He could be trying to use the time - travel chaos to his own advantage, like stealing forbidden jutsu from different eras.
Often, Orochimaru can still be a main antagonist. Even in a time - travel scenario, his thirst for power and immortality doesn't change. He might oppose Naruto and Tsunade's attempts to change the past as it could disrupt his own plans for power.
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.
Well, the main antagonists could be a group of rogue ninja who are hired by a powerful nation to take down Naruto. Since he is unkillable, they would have to use more underhanded tactics like trying to isolate him from his friends and allies. Or perhaps there is a dark force that is awakened by Naruto's unkillable state, thinking that he is a threat to the balance of the ninja world. This dark force could then become the main antagonist, trying to destroy Naruto at all costs.
Perhaps a new character could be the main antagonist. This new character could be a powerful ninja from another village who has some sort of connection to Konoha. They might be influencing Tsunade's decisions in a negative way, for example, by making deals that Naruto sees as harmful to Konoha. Naruto snaps at Tsunade because he doesn't understand why she is going along with this new character's demands. This new character then becomes the main source of conflict as Naruto tries to expose their true intentions and fix the rift between him and Tsunade.
It's Naruto and Tsunade. Naruto is known for his determination and his ability to make friends and influence those around him. Tsunade, on the other hand, is a strong - willed woman with great medical and combat skills. In this fanfiction, their interactions are likely to be the focus, with Naruto looking up to Tsunade as a mentor and Tsunade seeing Naruto as a symbol of hope for the future of the village.
Maybe there are powerful dark sorcerers. These sorcerers could be trying to capture Naruto for their own evil purposes, like using his power to open a portal to a dark dimension or something, and Kurama has to protect him from them.
Another type of antagonist could be a strict professor who doesn't like Naruto's carefree attitude and Hinata's association with him. The professor might try to give them a hard time, like assigning them extra difficult projects or being overly critical in class, which becomes an obstacle in their college life and relationship.