High Elves and the Balrogs

[Boromir88]

So would Galadriel not need to fear the Balrog of Moria, then (besides the necromancer in dol guldur)?~Gorthaur

Well it's not so much that Galadriel would not fear a Balrog (I think even Gandalf displayed fear towards Durin's Bane). As no matter how powerful you are, a Balrog is a tough nut to crack and not a foe anyone would look forward to facing.

But, if you are asking would Galadriel be able to slay a Balrog, I'd say she's got a pretty good shot. As Galadriel is tough in her own regards...not just 'magically' but also as far as fighting abilities go too:

'Galadriel was the greatest of the Noldor, except Fëanor maybe, though she was wiser than he, and her wisdom increased with the long years...and she grew to be tall beyond the measure even of the women of the Noldor; she was strong of body, mind, and will, a match for both the loremasters and the athletes of the Eldar in the days of their youth.'~Unfinished Tales; The History of Galadriel and Celeborn

and...

'Even after the merciless assault upon the Teleri and the rape of their ships, though she fought fiercely against Feanor in the defence of her mother's kin, she did not turn back.'~ibid

So, I would say Galadriel was someone who also knew how to use a sword. Giving her a 'pretty good shot' in my opinion.