How can I delete duplicate albums from my photo library?
Camera Roll, Photo Stream and Photo Library are system albums and cannot be deleted. (Photo Library is a smart album and displays all your photos, regardless of where they actually are).

Your photos are probably only in the iPhone album, if you delete it, they're probably gone. However to delete it hit the "Edit" button, then the little red minus in front of the album you want to delete.

If you added the album to your phone by syncing it from your computer, you won't be able to remove it from the phone. In that case connect your phone to iTunes select the photos tab and uncheck the album you want to remove.