How much is it to replace the battery in an iPad mini

iPad Battery & Power - Official Apple Support

What does battery service cost?

Your Apple One Year Limited Warranty includes replacement coverage for a defective battery, and there is no charge if your iPad is covered under warranty or an AppleCare product. You can check your coverage by entering your iPad serial number.

Out-of-warranty battery service cost:

All iPad models: $99

Plus a $6.95 shipping fee. Fees are in USD and exclude local tax.

Make sure you back up your iPad before you send it to Apple or bring it to an Apple Retail Store.