It is actually possible to earn this badge on the first day of you using Foursquare. Which was the case for me. I earned it along with my Newbie Badge, Adventurer Badge, and the Overshare badge.

Crunked Badge Foursquare

How exactly do you get Crunked? Its very simple actually, you just have to be out and about for one night. You are officially Crunked on Foursquare if you check in at 4 locations in one night. Now I do not know when Foursquare starts or ends the “night” but for me the 4 stops happened after 8:00 PM and before midnight

So if you are bar hopping or just out for the night, check in at 4 locations and you get Crunked