And Stay Out! Achievement in Little Kitty, Big City

This will assuredly happen naturally, but the easiest way is to go to grandma's market in the center of the map (marked with a carrot) and knock stuff over or jump around on produce. She'll grab you and throw you out, unlocking this achievement.

This can also be done at the construction site. Just run in and go to the worker until he picks you up and carries you off site.

Refer to Home Sweet Home! (50G) for a full video walkthrough!