Can be from any kind of media.
For me it’s Margot from The Magicians (which is interesting because in the books she is anything but) and Jesse Faden from Control.
Ellen Ripley. Under pressure she steps up and does what needs doing. Whether that means operating a loader, comforting a child or making monsters extinct.
Granny Weatherwax, Nanny Ogg, Tiffany Aching.
About half the cast of Fullmetal Alchemist (Olivier Mira Armstrong, Izumi Curtis, Riza Hawkeye, Winry and Pinako Rockbell, Lan Fan, Mai Chang, Chris Mustang… and I’m sure I’m missing some).
Oh, and friggin’ Chell, of course. Makes you almost feel sorry for GLaDOS.
Xena Warrior Princess
Leela from Futurama
The Boss, MGS
Not Big Boss, the man with the eye patch and is a bad guy, the woman who taught him and the mother of Ocelot
She was such a badass woman that she inspired basically everyone around her to try to mold the world in the way they thought she saw it. Shes a great example of a woman/mother who’s a badass directly because of the skills normally associated with those roles. Yeah, she can fight and kick your main characters ass, but that’s mostly because she’s spent time nurturing him and caring for him to the point where he emotionally cannot fight her. She regularly disarms strong, imposing men (some with superpowers like lightning channeling) by just looking at them sternly and implying she’s about to call them by all 3 of their names in a disapproving tone
Time and again she does badass things while she’s alive, and her death is technically the catalyst for the rest of the series as those who loved and admired her try to shape the world as she saw it, which isn’t even something she herself did because of her loyalty to her country.
Oh and she’s voiced by the same woman who does Pearl from SpongeBob, which is wild
Hermione Granger because I read so little fiction that this is the first woman (?) that comes to mind.
assuming that “strong independent woman” being in the title of the original post counts as someone saying it
Korra and Toph from Avatar, Tsunade and Sakura from Naruto
Samus came to mind immediately
Roberta “Bobbie” Draper from The Expanse was the first to jump into my head.
Appsros character in Abberation
Ripley
Garnet (Steven Universe)
Mirko!
Margot is also amazing, but she’s not independent IMO. She’s very emotionally hooked. Not in a bad way, mind you. She’s like a shounen protagonist who screams for 5 episodes because her friend was threatened and somehow a nation collapses as a result.
I mean, no one is really independent, but women in fiction tend to be very dependent on men as (almost) their primary personality trait.
I loved Margot because she was as independent as anyone in real life can be. She did her own thing, helped her friends, let her friends help her, fucked up, owned it and fixed it (most of the time, anyway).
All the characters were very realistic (well, if you ignore the magic).
I mean emotionally independent. Margot had some serious needs. Functionally she’s totally independent. Probably all of them except Fen were.
Hyacinth Bucket (ITS BOUQUET)
He might be a doormat, but she’d be utterly lost without Richard. As such, I can’t agree she’s entirely independent.
Adding to this, she’s also too concerned about what other people (her social betters not her family) think of her to be truly independent. She is strong, however.
Not the first that comes to mind, but I have to add Nausicaa into the mix. She shows her strength through nothing but kindness and determination, without the need for violence or cold cruelty. A frightened critter bites her, and she endures the pain to keep soothing it without interruption. Ripley’s a badass, but she’d never be able to do that.