I love how the gun sounds like an actual gun even though it's shooting nerf darts.
Anyway, the scoring for repeating hits on the snowmen are a bit weird. In theory, you should go around shooting each snowman in the head as fast as possible for the highest score, and thus the game rewards you for being as accurate as possible while being fast. But in practice, it's pretty hard to get all 15 points from a snowman while on the move, so the fastest way to get the most points possible is to just walk up to every snowman and shoot it repeatedly.
Or at least in my experience. By doing the above method, I was able to score 555 points (probably most of the snowmen, if not all) in 1 minute and 43 seconds. You may be able to get it faster if you're a god at first-person shooters though - keep in mind that my time also includes the time I wasted shooting snowmen that I had already hit.