Empowerment is perhaps not the right word; I’m looking for songs by female artists about overcoming adversity and affirming the speaker’s own self-worth. Thus far I’ve got “Beautiful” by Christina Aguilera and “Me” by Paula Cole. Any other thoughts?
“R-E-S-P-E-C-T”, Aretha Franklin?
Destiny’s Child - I’m a Survivor
Alicia Keys - A Woman’s Worth
And some others that you may think are silly, by Shania Twain
“I Will Survive” by Gloria Gaynor
“Out of Range” by Ani DiFranco (this is just the first of hers to come to mind; I’m sure she has others that qualify for the OP)
“Sisters are Doing it for Themselves” by Annie Lennox
I Am Woman, by Helen Reddy
Koko Taylor, I’m a Woman.
“How Dare You” by Basia
And not specifically feminine, necessarily, though it is in the original context, “Without You” from My Fair Lady.
“Love is a Battlefield” by Pat Benatar. Theme song from the woman-empowerment movie “The Legend of Billie Jean.” Not sure it’s quite what you’re looking for, but I’ll toss it out there anyway.
Bif Naked “I Love Myself Today”
Shampoo “Don’t Call Me Babe”
No Doubt “Sunday Morning”
There’s a cover version on the soundtrack to the movie “Trick” which is quite good, if you want somethnig a bit more up-tempo. Two covers actually, remixes.
I can’t tell if you’re making two separate Benetar suggestions, but the theme song from TLoBJ is “Invincible,” which is also by Benetar.
Holly Near, “Mountain Song / Kentucky Woman”
Peter Gabriel/Shaking the Tree
Sisters are Doing it For Themselves by the Eurythmics (mentioned earlier but I still love it!)
Independent Women by Destiny’s Child
Tori Amos – “Silent All These Years”
Madonna “Express Yourself”
D’oh!
Sorry about that. That’s what I get for posting half asleep. 
Retract my suggestion and change it to “Invincible.” Thank you.
And Aretha Franklin.
I’ll also nominate Tina Turner, “Better Be Good to Me.”
It’s an odd suggestion, but “Carrie” from Carrie - The Musical is about Carrie White’s plans and desires to go from a nobody to being memorable and remembered. There’s a version on Linzi Hateley’s (who originated the role) album “Sooner or Later.”
“I’m Beautiful” by Bette Midler might fit the bill.
“Hard Candy Christmas” by Dolly Parton from Best Little Whorehouse in Texas.
I think “Girls just want to have fun” fits, along with the more “serious” stuff listed.
also “I’m Gonna be an Engineer” by Peggy Seeger. Great lyrics, can be found here among other places: http://www.lyricstime.com/seeger-peggy-im-gonna-be-an-engineer-lyrics.html