The key here is to kill animal species. It's been proved that the four legendary animals are NOT required for this. Also, you do not need to skin the animals, just kill them. I've taken out domesticated animals and put them in a separate group at the bottom.
To find out what you have killed, press Start > Stats > Misc
Bear -Tanners Reach
Beaver - Northeast of the word Cochinay along the river. Also look south of Tall Trees in Bear claw camp (you have to zoom in real close to see the name, below Manzanita post).
Bighorn Sheep - Between Rattlesnake Hollw and Pleasance House
Boar - Can be found in pens at the most Nothern point on the map, in the snow mountains near an abandoned fort there.
Bobcat - Southwest Mexico, go to the bottom left corner of the map; around Escalera and Nosalida. Also found in the Northeastern part of the Great Plains.
Buffalo - Great Plains
Cougar - Southwest of Fort Mercer, Southeast of Repentance Rock
Duck - South of Gaptooth Breach, west of the Scratching Post along the water line. Also found around Lake Don Julio.
Eagle - Tall Trees
Elk - Tall Trees
Fox - Tall Trees and Great Plains
Horse - Wild
Raccoon - Must hunt at night as they are nocturnal, seen around Armadillo and packs in the Great Plains.
Seagull - Near Blackwater, you can hear its distinctive sound
Skunks - Around Armadillo
Snake - Found all over, be sure to listen for the rattle sound.
Vulture - Kill something and they appear flying over the dead animal
Domesticated Animals (not needed for the achievement)
Chicken - MacFarlane's Farm
Dog - At least one in every town
Donkey - Random mexicans riding donkeys
Goat - Mexican towns
Horse - Domesticated
Some info from Reddead Wikia: http://reddead.wikia.com/wiki/Hunting
The rest from awesome commenters. Thanks!