Tap the Start button in the Bullseye Challenge screen to enter the match. You can see how many Free Tries are available right above this button.

Once the game begins a moving target will be projected on the court, and a ball throwing machine will throw balls at your direction. The target is divided into three areas, and each area will grant a specific amount of points. You need to score a minimum amount of points to be able to unlock and claim a prize.
It is not possible to tap to move around with your character, so watch the target's movements to plan your moves!
Also, don't worry about using your best equipment. Your stats will not have any influence in this game mode and all players have the same stats!