1. Know your local laws. We don't advocate illegal activity on TFL. Period.
2. Be safe. Shooting things at close range with a firearm can be dangerous and discharging a firearm without a good backstop of some kind is dangerous. Be sure there's nothing behind what you're shooting at that could cause a ricochet or fragmentation and result in injury.
3. If you can safely and legally do something to end an animal's suffering, do it. A gun isn't the solution to every problem encountered. In some cases notifying the authorities may be the only option given the circumstance of the situation. In some cases it might be legal and safe to shoot the animal yourself. In some cases, there might be other ways to humanely deal with the problem.
And I think that covers it. We're not going to play: "Who's the kindest person to animals and therefore the best person here." If you know you are, you can feel good about it without having to publicly make the point, and more importantly, without having to denigrate others who can't possibly measure up.