Please Do Feed the Animals is the sixth event in the Wild West booth in free play. If you want to play it you need to play through the previous five events to unlock it, or play Adventure Mode and it will cycle to this booth eventually without needing to unlock it.
At the very end of the level a meteor starts falling towards the town. To destroy it you need to hit the three targets that are attached to it, but for this achievement, don't do that. Eventually the meteor will hit the town, it will be destroyed, and the achievement will unlock.