There are two very different types of fish known as "batfish."
Neither, IMO, are particularly easy to keep.
This is one type:
http://fishbase.org/Summary/SpeciesS...iesname=elater
This is another (note, often the dorsal and ventral fins are very elongated to give the common name batfish - but mostly in juveniles, the much larger adults don't usually have the large fins, or pretty color)
http://fishbase.org/Summary/SpeciesS...sname=pinnatus
I have limited experience with both types, but neither was good.
What size tank do you have, and what other fish do you keep?