This is the Boar Riding achievement. Shortly after being able to run around the first village and chat with people, you will get a side-quest called "Boar Hunt" from an old man on the left side as you enter the market district in the first town. This quest sends you to kill a wild boar that is near the entrance to the Aerie in the Northern Plains. It's a pretty beastly foe- if it manages to catch or wing you with its charge attack it will take off the majority of your lifebar and it has a ton of health. The best way to kill it is to just get in a small area like the tight area leading toward the Aerie gate and keep dodging. It will slam into walls and knock itself silly- take any opportunity when it falls over to use the "attack enemy on the ground" technique (block+X) as this will do a large amount of damage. Play it safe- its charge can hit you even if you are hitting it from the side at times.
Once you kill it, loot it and return to the old man and he will mention having a boar horn in your possession will allow you to ride boars. Now, anytime you go into several different areas such as the northern plains, there will be boars laying on the ground which you can mount with B and drive around- charge with A and bank left and right with right and left triggers. To get the achievement you must ride a boar for 5minutes straight. If you bump in to a rock or something or get winged by an enemy while riding the boar you will very likely get knocked off and the timer will reset, so simply get on your boar, find a peaceful area with no aggressive enemies around and go get a snack. It is boaring, but after 5min the achievement will pop.