Given the name's sound (and its meaning, as I later felt), I'd say it suits a boy better. Just swap the ending "-e" for "-os" and it can go perfectly on a son.
I've always pronounced this "an-DROM-ah-kee", like Andromeda with an "akee" instead of the "eda". I think it's an absolutely gorgeous name. I'd love to use it some day!
"Battle of a man" really makes no sense to me. "Fighting man", perhaps, but not as a female name. "Fights like a man"? Also unlikely. And the character in the Iliad is the model of a soldier's wife - loyal, supportive, warm and loving; not a bit aggressive. Perhaps it could be something like "Belongs to a man of conflict", which makes us shudder but would have been A-OK in antiquity.