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.
Buffy. I was the right age (or maybe a bit too young) when it aired and it was the first female-led show that I fell in love with.
Princess Cimorene from the Enchanted Forest Chronicles
Very good chocolate cake recipe from that series. Very chocolatey.
Ron Swanson
Susannah Dean and Naomi Nagata
Zoe, Inara, Kaylee, and River. Mic drop.
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.
Leela from Futurama
Taarna
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.
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
Roberta “Bobbie” Draper from The Expanse was the first to jump into my head.
Avasarala is my pick
Came here to say Avasarala.
That’s funny. I also posted Naomi Nagata. While I like Chrisjen and Bobby more, I think Naomi wins for strong independent. General of the resistance, self-marooned insurgent, and the escape of the Chetzmoka.
Xena Warrior Princess
Korra and Toph from Avatar, Tsunade and Sakura from Naruto
Samus came to mind immediately
Ripley