what does battery replacement for an iPad Air 2 cost

As was posted, $99+tax in the United States. Also a shipping charge if they need to order it. Perhaps different in other parts of the world. Also - they don't actually replace the battery because it's not something that is easy to do in a store. They really offer a complete replacement with a new/refurbished iPad. The returned iPad would then be sent to a service center to get a new battery for another customer to receive a refurb. So if you do it make sure to back up all your data so you can restore.

Also - if there's any kind of engraving done by Apple, they can have that applied to the replacement iPad, but you'll need to wait for shipping. They also won't accept one for a battery service if it's damaged.