In the Animals and Friends booth, you will come to the Hamm and Eggs mini game.
To bring out the mouse, you will need to shoot two groups of pigs. The first group will have four pigs and the second group will have three pigs. After you have hit the last pig on the second set, the mouse will come out from behind the windmill. You can do this a number of times if missed.
Video Credit goes to OnceFallenPS3T