There are several videos on the internet that explain how to replace the battery.   Removing the back just takes some patient work with a small thin tool, like a screwdriver. 

I've seen other posts that say you can sometimes fix a phone that got wet by putting it in a bowl of uncooked rice for a few days.  

Hi Jeremy, sorry to hear that about your wife's phone. The thing wit hthe Motorola Droid Mini is that it has a non-removable battery, so the back cover is really sealed shut. The way to remove it would be with the use of special tools, for which you might need to visit a repair center or some kind of mobile phone repair professional. Have you tried looking into those yet?