Throughout The Kid's adventure in his post-Calamity world, you'll come upon special items that he can used in the Forge to upgrade an assortment of weapons. The following materials are used for the corresponding weapons:
If you upgrade the bow to have +50% damage (the second bow upgrade), you can destroy the targets in one shot, without the need for a power shot. This makes the gold medal much easier. If short on upgrade materials, a bronze medal will give you one something stringy upgrade material.
When having trouble with the Slinger Range Proving Ground, keep in mind that you can't get negative points. So, shooting a little bit before the first target shows up can get you a couple extra points that can make all the difference when going for a gold medal.