The adventurer badge is most likley the second badge you earn on Foursquare, and you could earn it shortly after you earn the Newbie Badge.
Adventurer Badge Foursquare
The Adventurer badge is actually fairly easy to earn and can be earned quickly. All you have to do is check in to 10 different locations, and its yours.
I managed to unlock this badge on the same day as my Newbie Badge. Actually with a few more check ins, you can actually get two other badges, the Crunked and Overshare badge, which I did, Yikes 
