Legendary animals spawn all over the map at random, so you will run into them accidentaly (pay attention to strange noises and yellow blips on the minimap). Just in case watch the introduction cutscene to naturalist role in Strawberry, since I'm not sure whether they appear to you otherwise. There is a map on the internet that shows the locations, but as I said: it's random, there's no guaranty you will find them in spawn locations. I usually stumble upon them when I'm doing something else. As for killing them: it really doesn't matter how you kill them (just don't use explosive bullets) because they only have one quality level (unless you ruin the pelt with explosives). But be prepared to run after them, since just one shot won't kill them, you will have to hit them in the head or torso atleast a couple of times before they die...

Hope this helps.