So I used my VAT to headshot a Legendary Glowing One with a Combat Shotgun to kill it easily. When it died it just went through the ground. I caught it on tape. Since I can't post links here, My YouTube channel is Vqtr and you'll see it there.

Legendary critters are fairly common enough. i would suggest if you want that specific Legendary critter, wait till the game respawns that area and go back and try it again.
the item it drops will be different each time, at least the epic mod on the weapon/ armor will be different. it's randomly generated and there's like 40 special effects it could get, and it only ever gets one of those, according to the page in the strategy guide i glanced at.

Ok thank you very much!