Sort balloons by end point. Shoot an arrow at the first balloon's end.
This bursts all balloons that overlap with this position. Skip all balloons that are burst. Move to the next unbursted balloon and repeat. Why shoot at the end? It maximizes the chance of hitting other balloons. Any balloon starting after this position will need a separate arrow. Delaying the arrow wastes the opportunity to burst overlapping balloons. A balloon's start might not overlap with others, but its end is as far right as possible while still hitting it.