Far Cry Primal

There are total 17 tameable beasts in Far Cry Primal. You need only 7 of them for the achievement. (tame 7 times the same kind of animals does not count!)

To tame an animal, you must use a bait and then go slowly in front of the animal, press and hold X before it finishes eating the bait. For the later enemies you need some skills from the beast hunter skilltree and the last 3 beasts are only available with the Beast Master Hunt sidequests. Rare animals have a scent trail when you use Hunter Vision, so you can easily spot this kind of enemies. For the location of any beasts look on your map for the animal symbol. The symbols / animals are switching with the Day / Night cycle in Far Cry Primal.

Here is a showcase video with all 17 beasts

Just like the achievement says, tame 7 beasts. You'll gradually be increasing your numbers as you gain more taming ability as it opens up more options for you to ambush and plan better in combat anyway.

In order to tame a beast it's the same as the introduction method was, toss some bait wait for the beast to start feeding and crouched walk towards it and hold down when the prompt appears until the taming is complete.