Aim and fire an arrow from the bow, which then subtly strikes the cowboy.
If you succeed, you will get to the next level, which is harder and harder.
Be careful to do it all, because if not, you will have to repeat the level. There is also a limited number of arrows available, so try to make the best shot.
At the same time it must not happen that you crash the cowboy on the turn, because thats how his death really accelerate.
Enjoy!