Far Cry Primal

You need these two skills for the Achievement. In the Beast master skilltree the skill "Tame Apex Predators" and in the Fighting Skill Tree the Beast Rider Skill. Tame a brown Bear or Sabretooth Tiger (look on your map for the locations). Now kill 25 enemies while riding your beast. Both beast kills and weapon kills count.

Ok for this Achievement it requires one of two things, either be riding a Mammoth or to be riding a saber tooth tiger. Both skills are in the second row of the fighting skills tree portion. Once you have either it's time to start riding the mount of your choice, if it's the saber tooth tiger, you'll also need the Tame Apex predators feature. So it's actually easier to do this with a Mammoth as it would take less effort. Either way mount up and slaughter 25 enemies in order to make the achievement pop. As long as the game registers the kill as "Mounted Kill" it will be counting towards the achievement!

On the mission "Stomp Umad" you have to go to a camp, get on a mammoth and destroy the bone trees. If you don't destroy the bone trees then enemies will continuously spawn. You go use the animal charge or your own weapons, both count.

By far, the easiest way to do this is on a mammoth. At one point, you will have to mount a mammoth and crash through a gate in a canyon to go further south. Once you've done this, just travel around the region and you'll regularly encounter enemies in groups of 2-3. Charge with the mammoth and then click RS to take any stragglers out with the mammoth's melee attack. You can also take out enemies from its back with your bow and those will count towards your total.

You could also do this in the north, but the terrain is a lot rougher and it's harder to navigate with a mammoth.