1) Lower the shot distance that makes the mobs run/aggro. There could be at least 3 rotations if the effect was lowered a bit.
2) Change the terrain to be shorter grass. Because of the sloping terrain, the longer grass create a lot of problems visually.

3) Add some graphic indication that the mobs are aggroing you, and not simply running in your direction. It makes no sense that an animal would run in the direction of the shot when not shot themselves, but that's a different issue.
4) Add some kind of effect to hawk corpses. Because of the mini-game, you can't always see where they fall. They also get stuck in trees, off the sides of cliffs, etc. Some larger graphic showing their spot would be helpful.

5) The terrain below the quest giver also has a lot of holes that the mobs will fall into and desync. The atrocious bear [still incorrectly named boar] will often run under the ground after being shot and then reset over and over until you find a direction it can move without resetting.

6) Not LoML specific, but make the yellow part of the mini-game larger based on your hunting level. There should be an advantage to having a higher hunting level, and making the mini-game easier seems like an easy one.

edit:
7) A pet that will drag the corpses close to you would be a cool thing too. Hunting dog or something to drag them to you. You'd still have to butcher them, but not run back and forth for them.