Perhaps they time travel to a period when a great evil was first emerging. They then have to figure out a way to stop this evil from taking root without using the knowledge and power they have in their own time. This could involve finding and training local ninja in the past to fight against this new threat, and in the process, they learn new techniques and strategies that they can bring back to their own time.
Maybe they travel back to a time when Tsunade was just starting to develop her medical ninjutsu. Naruto, with his understanding of modern medical knowledge (from Sakura perhaps), could help her make great leaps in her medical skills. They could also team up to deal with a powerful enemy that was a threat at that time. Naruto's strength combined with Tsunade's budding abilities would make for an exciting story.
In Juubi Naruto time travel fanfiction, plot twists can be really exciting. For instance, Naruto might find out that the Juubi has a different origin in the past than what he thought. This could completely change his perception of the tailed beasts and his role as the Jinchuriki. It could lead to him having to form new alliances or fight new enemies in the past.
One possible plotline could be that Naruto accidentally travels back in time and lands right in front of Tsunade when she was at a crucial point in her life, like just after the death of her loved ones. Naruto, with his future knowledge, helps her cope and in the process, they grow closer. Another plotline could be that Tsunade is sent to the future where she meets an older and more mature Naruto. They initially clash due to their different outlooks from different times but then gradually fall in love as they understand each other better.
A Naruto and Tsunade time travel fanfiction can be really interesting. It could involve them going back in time to change certain events in the Naruto universe. Maybe they go back to prevent a great tragedy or to save a beloved character. For example, they might travel back to the time of the Uchiha massacre and try to stop it, which would completely change the course of the story.
One possible plot twist could be that Naruto's Mokuton abilities attract the attention of Orochimaru. He might try to capture Naruto to study his unique power. Since Tsunade raised Naruto, she would be extremely protective and engage in a fierce battle with Orochimaru to keep Naruto safe. This would not only test Tsunade's strength but also Naruto's growth under her care.
A plot twist could be that Naruto discovers a secret about Tsunade that she has been hiding all along. It could be something related to her family or a power she has been suppressing. This discovery could either strengthen their relationship or create a rift between them. Also, there could be a twist where an outside force tries to use their relationship to gain power in the ninja world. They might try to manipulate Naruto or Tsunade to their advantage.
Since it's a fanfiction, there could be all sorts of plot twists. Maybe the hospital is secretly a front for some illegal ninja experiments and Tsunade has to uncover the truth. Or perhaps a long - lost relative of Tsunade shows up at the hospital with a secret that could change everything in the Naruto world. Without reading it, it's all speculation though.
One possible plot twist could be that Naruto and Tayuya travel back to a time when the Hidden Leaf Village was first founded. This would put them in the middle of the early power struggles and they might have to use their future knowledge to prevent a great disaster. For example, they could stop a rogue ninja from stealing important village secrets that could have changed the course of the village's history.
One possible plot twist could be that their time travel messes up the existing timeline in ways they didn't expect. For example, they might accidentally prevent important events from happening in the past that were crucial for the future they came from. Another could be that they find out they were meant to time travel all along to fix a long - hidden problem in the ninja world's history.
Also, in the past, they might have to adapt their fighting styles. Naruto, used to fighting with his friends and allies from his own time, now has to work with different ninja in the past. He may have to learn new teamwork strategies and combine his abilities with those of the past - time ninja in a different way. Tsunade might also have to rely more on her brute strength and less on her developed medical and strategic skills from the future, at least until she can adjust to the past situation.