Please don't take this the wrong way, but these types of posts really concern me.
Why are you shooting animals that are just trying to survive?
Those guns hurt horribly, and that's on a person. The chipmunks or the squirrels are native, and your cats are the invasive species. Outdoor cats each kill hundreds of birds and small animals a year as it is.
It is completely natural for squirrels to eat birds' nests. The bird populations are long adapted to endure occasional nest predation. The issue that results in their decline is the unnaturally large numbers of cats in urban settings, most of which are fed and able to live at very high population densities but which still kill for fun. Birds can't deal with that pressure as well. In many areas, cats live at densities 10x or more that native predators would have lived at. That is a lot of pampered predators to avoid.
We don't have many outside cats here thankfully - coyotes moved into the city a few years ago, and killed most of them. And we have never had so many birds as the past couple of years. I saw my first oriole, and several species of warblers this spring!