This side-mission will not become available until the mission, "The Shootist" (The Malibu Club Asset) has been completed. This will be available from the shooting range in the Downtown Ammu-Nation gun store.
The same deal with the aforemented mission is manifested in this mission - beat the high score. Only the main shooting range, the first part of the mission's objectives, is used, and your target for completion is halved to thirty points. That seems easy enough.
However, the real aim here is to score 45 points. This is where the challenge comes in. This is required for 100% completion, but isn't explained in the game; so now you know.
The nearest target scores you one point; the middle target scores you two points; and the farthest target scores you three points. You have two minutes and 100 bullets. This may be difficult, but this is how you should go about this.
The targets have five areas - four of them being the "body", and the "head" as the fifth. The targets can get in the way of each other, so if you were to shoot out the "bodies" of all but the further target, you will have a clear shot for three points. All that's left is for you to be a good shot. When you come down to your last few shots, shoot the "heads" off of the other targets to finish up and score some extra points.
Reward
Your outright reward for scoring 30 points or more is $500. But, scoring 45 points or more will unlock the Fast Load Feature. The reloading time for your weapons is eliminated, allowing you to fire continuously until you run out of bullets.