A lot of what Tolkien wrote about Middle Earth comes in broad strokes and he left unpublished many contradictory accounts. We know broadly what happened in the Second Age but exact events are not set in stone. In one of his letters Tolkien wrote;
Now assuming "the elf lady" you are talking about is Galadriel, Christopher Tolkien wrote in the Unfinished Tales,Originally Posted by Tolkien
In letters Tolkien called Galadriel an "Amazon," something he likened to a soldier. She was certainly active in combat during the First Age and it isn't hard to imagine this version of Galadriel continuing as a warrior through the conflicts of the Second. It's worth noting that all elven women will fight in defence but usually only the men will actually go forth in attack. Galadriel was noted as being more like a man in her pursuits, competing athletically and desiring to rule a region of her own in Middle Earth.There is no part of the history of Middle-earth more full of problems than the story of Galadriel and Celeborn, and it must be admitted that there are severe inconsistencies "embedded in the traditions"; or, to look at the matter from another point of view, that the role and importance of Galadriel only emerged slowly, and that her story underwent continual refashionings.
Also don't be surprised to see her kicking major amounts of arse. The Sindar (elves like Legolas) were more powerful in those days, the Noldor (Galadriel's faction) were said to be as far above the Sindar as the Sindar were above men, and Galadriel was greatest of the Noldor.