Holy cow this game is awesome. I LOVE the idea and the potential in this alone makes this one of my favorites so far.
A couple of ideas: I think the tension would be greatly increased if the monsters still moved while you were golfing. I found it too easy to dispatch of them before I started golfing which made it feel like two separate games almost. But if you combine them? Man... That would be something.
Contributing to that, I think it would be great if hitting the monsters with the balls was the main way of defeating them. Maybe the golf club stuns them/knocks them back and the golf balls finishes them off? Ugh, I'm drooling at how cool this idea is.
All of this is up to you, of course! I also really enjoyed the art. Thought it looked great.
One critique: For whatever reason I didn't feel like I was ready to move on to the next level when I HIT the goal with the ball, because to me, golf = ball in hole. I was more confused than anything that the path opened up once I hit it without actually sinking the putt. This is simply fixed with resetting the par count and some kind of better indicator that it's time to move on.
Overall, incredible job. You're getting high marks in my rating.