Batman has trained his body to the very limit of the human condition. But as he is still human, he is bound by certain laws that work against it. One such being he can't breathe underwater. Though he can hold his breath a long time.
But when longer stays in a body of water is needed, he pulls out his Rebreather, a device that allows him a near unlimited time in water without the need to go back to the surface for oxygen.
In fact, the rebreather has been a part of Batman lore for years, including being a part of the Batman '66 TV show, and numerous comics, movies, and animated TV shows after that.