There are two ships to fight while inside The Vault. In the middle there is a Mogai, simply hug the wall and you won't have to fight it. At the end there is a Bird of Prey, continually fly right below its belly and it won't fire torpedoes at you - making it fairly easy to kill it after a minute or so.
I have done this 10 times (twice on each of my 4 characters solo (fed: 1 sci, 1 eng, 1 tac, Klingon 1 tac), and twice more in groups). I have used every shuttle available, the klingon thing (forgot the name), Type 8, Runabout, Delta Flyer, and that D'Kyr shuttle thingie