The multiple kill achievements may be a little difficult, especially 3 and 4. I would recommend playing through the game fully, so the animals are more plentiful, so the Compound Bow is unlocked, so you have improved accuracy, and have the sniper training equipment so that the animals don't run. Once you've done that, I would recommend going to America or Europe on Master with either the Compound Bow or Blowgun (I personally used the bow). Once you find a screen with 4 or more animals on it, focus on killing them with 1 or 2 quick shots. The other animals standing around shouldn't run away, so once you kill the first animal, move on to the next one and go again.
This will also work on lesser difficulties all the way to Rookie, but sometimes it's harder to get 4 animals in one scene on Rookie.