This is best accomplished in the Coastal Forest region, hunting either deer (the first half of the region) or wolves (the latter half).
In both cases you will need to use powerful shots from the bow. Tapping RT will not cause enough damage to kill the animal. A full power bow headshot on a deer will kill it in one shot. A full power headshot will NOT kill a wolf. Be prepared to shoot them multiple times (thanks to Kaiser679 for confirming).