1. rude slang To become uncontrollably or unreasonably irrational; to act in a wildly irrational manner. The drivers in this country seem to go completely batshit if there's even a little bit of snow on the ground. If they get too much sugar, the kids start going batshit and start running around the house screaming.
2. rude slang To become wildly or uncontrollably angry. My parents went totally batshit when they found out I'd wrecked the car! Now, don't go batshit or anything, but I've decided to move to Canada.
3. rude slang To become extremely excited or enthusiastic (about something). I've never understood that pop star's popularity, but kids just go batshit over her music.