I've been playing this game for so long that I made up a name and backstory for the character in my head: Robert Garriott, former park ranger turned invasive species population controller. Yeah, for some reason this guy really seems like a Bob to me.
The flying bell and chick walking along the ground are some good places to aim for to get lots of points. They both require multiple hits, meaning you'll have to give up some egg shots.
@Tiberiumshox: You may have noticed that the path continues on to the east. Keep going that way (maybe after going back and resting at the inn) to continue the quest chain.