The best way to get a lung or a heart shot is to use Infrared, which you can do while scoped in on an animal with your Rifle. This will reveal the Heart, Lungs, and Brain of the animals in the hunt, allowing you to precisely target the vital organ you need. Experienced players may find that they don't actually need infrared to hit a vital organ as a shot to a vital will count whether or not infrared is activated.

Infrared has a limited duration, based on the weapon used. Not all weapons come with Infrared. If you are finding that your weapon does not have enough Infrared to complete a mission, consider upgrading its duration in the Loadout.