Level 4-15 is the first boss battle in the game so far. Take note of his movement. He flies in somewhat of a pattern, so time your shots accordingly. This final level also introduces you to a new bird type as well. These birds, when you tap the screen, will fly in a horizontal plane.
With your first shot, aim low. It's easier for the boss to dodge you if you aim too high, so aiming low is your safest bet. Try to hit the boss in the chest. The more direct the hit is, the more points you will get.
On your second shot, you want to aim for the closest set of TNT boxes in relation to the sling. Wait to take the shot until the boss is right in front of you.
The third shot is with the cluster bird. Aim directly at the boss, and try to get all three of the birds, as they split, to hit him. Destroying the boss within the first three shots will result in a 3 star score.