This one is accomplished by grilling raw meat while on a hunt or expedition. You can only carry 10 raw meat on you at a time, but you can always go into your tent to get more.
In order to grill meat, select the BBQ Spit and use that item. If the BBQ Spit has a red X, that means you are out of raw meat.
There are two tricks to grilling the meat, depending on your preference. The first is to listen to the music. If you push the stop button (B on an XBOX controller, not sure on keyboard) two beats after the music stops, you will make Well-Done Meat and the characters will say SO TASTY!
The other trick is to watch the rotation of the meat. Make sure to push the button between the 3.75 and 4 rotations place. The handle starts at the top and goes counter clockwise.
If you push the button too early, you will get rare meat. If you push the button too late, you will get burnt meat. Both can still be used, but doesn't count towards the achievement. Use these two items to help you figure out your timing.