One idea could be that Batman, in his quest to fight crime in Gotham, discovers some sort of interdimensional rift that leads him to the world of The Avengers. He then has to team up with them to stop a common enemy that is using technology from both universes to cause chaos. For example, Loki could be teaming up with some of Batman's rogues gallery like The Riddler to create complex puzzles and illusions that are both magical and technological in nature.
Maybe in a fanfiction, Batman's detective skills are needed by The Avengers. After a series of strange events that seem to be both super - natural and criminal in nature, they call upon Batman. He arrives in their world and starts to analyze the situation. He quickly realizes that there are similarities between the threats in his world and theirs. Together, they form a plan to take down the bad guys by using Batman's strategic mind and The Avengers' superpowers.