For this achievement all you need to do is start the quest to kill 5 "bear's", kill them and then return back to the quest man. The quest and the bears can be found in the very top right of the map. Just walk next to the person with the quest, he will ask you to kill 10 bears which you will find are running around next to him. You will be able to kill them easily by head-butting them and more keep respawning as you kill. Once you have killed 10 go back to the person who gave you the quest and the achievement will pop.
If you would like a visual guide of how to find the quest or a video guide for the whole achievement I have included my video guide below.