How to get kicked out of a store in Little Kitty, Big City

This is the easiest and most reliable way to get the "And Stay Out!" achievement. Head towards the construction zone, which is a fenced-in area near where you first meet the Tanuki. You'll see a construction worker patrolling inside. Simply get in their line of sight and they'll chase you down. Let them catch you, and they'll pick you up and toss you out, awarding you the achievement! (Though technically not a store, the game recognizes it as one for this achievement.)

If you prefer a more chaotic approach, head to the small supermarket with the black-and-white cat. Talk to the cat, and they'll mischievously ask you to knock over three jam jars. Do their bidding and watch the destruction unfold. However, to get kicked out, you'll need to stick around after causing the mess. The shopkeeper will eventually get fed up and pick you up, tossing you out of the store.  Note: This method might require more patience compared to the construction yard approach.

You mentioned another achievement involving banana peels. Keep an eye out for bananas throughout the game. If you manage to use one to make a human slip, you'll unlock another achievement for your troublemaking kitty!