She might run into a group of rebels. If the alternate dimension has some sort of oppressive regime, there are likely to be rebels fighting against it. Amy could get involved with their cause and help them in their struggle.
She might encounter strange creatures. For example, in many alternate dimension stories, there are unique beings that don't exist in our world. Maybe she'll meet a talking animal or a floating jelly - like entity.
Well, she might encounter different versions of her friends. Maybe a Sonic who has a completely different personality or abilities. For example, he could be a dark Sonic in that alternate dimension.
Maybe Amy discovers a magical portal in her attic that leads to another dimension. In that dimension, the laws of physics are different, and she has to adapt quickly to survive. There could be strange creatures she befriends or battles against.
There could be a wise old wizard - like figure in the other dimension who guides Amy. He has lived for centuries and knows all the secrets of this strange place.
In the alternate dimension, Naruto could find that the Akatsuki are actually the protectors of the villages. This would completely change his view of the world. He would have to re - evaluate his ideas about good and evil and decide whether to help them or oppose them depending on their true motives.
Perhaps he'd meet a different Hokage. One who has led the village in a completely different way than in his own dimension. Naruto could learn a great deal from this Hokage about leadership and different ways to protect the village.
Barbara Gordon could be a great focus in a 'batfam alternate dimension fanfic'. In an alternate dimension, she could have different abilities or a different role within the Batfam. Maybe she's the one who discovers the alternate dimension first and has to figure out how to bring the others there or get them back. And of course, Alfred is also popular. His loyalty and his role as the family's caretaker can be explored in new ways. What if in an alternate dimension he had a more active role in the superheroics, like being a secret weapon or having special powers of his own?
One idea could be that in the alternate dimension, the Batfam members have swapped personalities. For example, Batman is overly optimistic and carefree while Robin is brooding and serious. Another plot could involve an alternate Gotham where the city is a utopia, but the Batfam has to deal with a new kind of threat that thrives in this perfect environment. Maybe a villain who wants to bring chaos to this idyllic Gotham.