For LeapPad1 and LeapPad2: From the Home Screen, tap on the child’s name or picture at the top of the screen.

This will bring up the “About Me” Screen. Look for the "Badges" field, and this will contain the total number of badges earned for the current profile.

For other LeapPad tablets and LeapFrog Epic you can click on the star icon on your childs home screen.  Visiting the rewards store will require a WiFi connection on WiFi enabled tablets.