Major Motoko Kusanagi.
I can’t decide if she counts though, as she is a cyborg who looks like a woman rather than actually being a woman. To be perfectly honest, I can’t think of anywhere in the universe that it is stated that her brain is even from a female donor.
And there is nothing self-serving or self-glorifying about their actions. They simply see that a job has to be done and they do it.
I wanted to mention ger but didnt know of animated characters counted. That is an excellent show
The Bride (Kill Bill), aka Beatrix Kiddo
She definitely has a human brain; the central theme is that she doesn’t know her own identity