You'll earn this achievement on day four. You will be tasked with looking after a Soviet officer named Igor, who becomes quite the handful.
If you respond to all of the radio calls relating to Igor, you'll earn this without any problems. But to detail the process, just in case -
To begin with you will be called to the Liquor Store. You will send Igor on his way to get some food, then later be called to the Moonwalk diner. You won't find him in there, but will be told that he's gone to the Donut store.
After leaving the donut store you'll receive one final call as Igor is causing a bit of a scene at the porn store. Thanks to this trouble you'll end up owing the store owner, Froggy, a big favour.
A squad car will then come to pick up Igor and you'll earn the Slav Squat achievement for your babysitting troubles.