You get this achievement by giving Farengar, a court wizard of Whiterun, the Dragon Tablet you find after using the Golden Claw to open the last part of Bleak Falls Barrow.
This achievement is a part of Objectives: "The Golden Claw" and "Bleak Falls Barrow". But can easily be accomplished by thoroughly completing "The Golden Claw", as "Bleak Falls Barrow" just has the Jarl of Whiterun having you talk to Farengar who then asks you to aid him in his research of dragons. After some talking to the wizard he will ask that you go retrieve an item from the Barrows called the "Dragon Tablet", if you already collected this item when you finished the Golden Claw objective you'll automatically finish this one and you'll get this achievement.
I also believe this is a story based achievement, so you'll need this to move the main storyline along.