Fun fact: as iPad batteries are glued[0], when requested Apple won't renew the battery alone and do full machine exchanges (but charge for the price of the battery only). So if you ever update your iPad 3 battery you'll probably need to do local backups to keep your apps if they got removed from the Store or you need a specific version.

Otherwise that's 50+ steps of fun to change the battery yourself: https://www.ifixit.com/Guide/iPad+3+Wi-Fi+Battery+Replacemen...

[0] at least before the latest models ? Did they stop doing that ?