The Elder Scrolls V: Skyrim Special Edition

You're guaranteed to get this just playing through the game at your own pace. However, the earliest opportunity is upon arriving in Whiterun following the following points.

Watch the opening scene, escape Helgen and follow Ralof or Hadvar to Riverwood. In Riverwood speak to Lucan Valerius and receive The Golden Claw quest. Follow the quest markers through Bleak Falls Barrow, making sure to collect the Dragonstone from the boss chest by the Word Wall. Then take this to Whiterun and speak to Jarl Balgruuf the Greater. Balgruuf will send you to see his court wizard Farengar who will then ask you to retrieve the Dragonstone which you can immediately hand over. When speaking to Balgruuf after this to claim your reward you will be interrupted by news of a dragon attack just outside of town. Balgruuf then sends you to kill the dragon.

Follow the guards out of Whiterun to the watchtower and kill the dragon. Shortly after its body has disintegrated you will absorb it's soul and unlock the achievement.