Galadriel did not 'single-handedly' fight off the attacks from Dol Guldur.
JRRT writes:
"After the fall of the Dark Tower and the passing of Sauron the Shadow was lifted from the hearts of all who opposed him. but fear and despair fell upon his servants and allies. Three times Lórien had been assailed from Dol Guldur. but besides the valour of the elven people of that land. the power that dwelt there was too great for any to overcome, unless Sauron had come there himself. Though grievous harm was done to the fair woods on the borders, the assaults were driven back; and when the Shadow passed, Celeborn came forth and led the host of Lórien over Anduin in many boats. They took Dol Guldur, and Galadriel threw down its walls and laid bare its pits, and the forest was cleansed."
LotR App. B.
She also was not the oldest living Elf in Middle-earth.
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Tar-Elenion
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