Everyone in this thread is talking about killing the legendary deathclaw from ridges and from afar when he is actually stuck in a caveroom in the dead wind cavern?
How could you possibly kill him from afar?
Anyway, use the fatman, or this is how I killed the bastard:
1. Kill everything besides him in the caverns.
2. Sneak to the opening and fill it with mines.
3. Shoot at him so he starts to chase you, preferrably with a missile launcher or a fatman to heart him even more, then he runs straight into the mines.
4. When his legs are crippled, kill him.
I did do this but also hit him wit ha second fatman after he had rushed into the mines, he survived that as well but got killed by the combined fire from me, ED-E, Cass, Boone, Raoul and Arcade Gannon.
Or you could use a hunting or riot shotgun and the "and stay back" perk.