Fortunately, the iPad Mini inherited the connector-fastened battery from its larger sibling, not the soldered-in battery found in the iPod Touch.

A plastic card makes a nice tool to pry the battery up from the rear panel, but it's still a very difficult task to break through all of the adhesive securing it to the rear case without puncturing the cells.

A close-up of the battery connector exposes the numbers 821-1564-04 C 3312.