In the Tea Cup Court alley, you will find the mini game called Hitting Streak. This game requires you to hit a series of 10 baseballs that are pitched to you by the Monkey in various speeds and techniques.
If you time your swing correctly you will hit the ball. Your technique and timing will determine whether you hit a single, double, triple or home run.
To get this achievement, you have to perfectly hit a home run on the final ball which is delivered at 100MPH. The machine that fires the balls has countdown lights on it. A good technique to hit the 100MPH ball is to swing just after the final light illuminates. The 100MPH ball comes very quick and is rather hard to hit. Ultimately, it is more luck than judgment!