Instructions
Target the Deathclaw from a distance, if possible, using the Anti-Material Rifle or the Sniper Rifle.
Aim for the Deathclaw's legs when firing your initial shots. If you can deal enough damage to the creature's legs, you will cause it to become crippled and unable to move towards you as quickly.
Aim for the Deathclaw's head once you have damaged its legs and continue shooting the head until the creature dies. It is best to use Armor Piercing or Incendiary shots when firing at the Deathclaw, as it is more vulnerable to these types of rounds.
Be sure to run backwards while firing at the Deathclaw, to help keep it as far away from you as possible. The strength of the Deathclaw means that even a moderately armored character can die from a single attack from an adult deathclaw.