How much does it cost for iPhone 12's battery replacement

$99 (U.S) plus tax.

Make an appointment if you are going to the Apple Store. No appointment needed at most authorized Apple service shops.

Call to make sure that the shop has a replacement battery in stock.

You can find a list of authorized Apple service shops in your area using this link: Find Locations

Plan to drop the phone off and pick it up again in an hour or two. it depends on how busy the shop is at the time. Sometimes you can get lucky and turnaround time will be 25-30 minutes.

Here is guidance on replacing a battery→iPhone Battery Replacement - Official Apple Support. It can frequently be done while you wait.