This is a story-based achievement which cannot be missed. You'll get it at the end of the Prologue.
Essentially, you have to complete the main monster quest of the prologue, including getting the quest to kill the griffon from the commander of the fort, doing the subquests that allow you to find out where the griffin is and how to attract it, actually kill it, then return to the commander for your reward. After that, once you return to the tavern to pick up Vesemir a cut-scene will kick-in and you'll get the achievement after that.
You can't really go straight in and do this. You'll likely want/need to explore the area a bit and do some side quests to build up a few levels before you can actually kill the griffin.