This achievement is easily attained during Mission 2: Welcome to the Jungle. You’ll reach a point near the very beginning where you go outside. Make sure to equip an explosive bolt, like super-thermite, and use invisibility to not scare the deer away. Aim using your bow, and hit the deer.
If you didn’t have an explosive tip at this point, don’t worry, you will see plenty of deer during mission 3, as well as other parts of the game, just keep an explosive tip on you at all times, or once you beat the game, just replay mission 2.