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.
Susannah Dean and Naomi Nagata
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.
Zoe, Inara, Kaylee, and River. Mic drop.
Leela from Futurama
Taarna
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
Ellen Ripley from the Alien series.
Linda Hamilton - Terminator
I had to say something different, because I would have said Ripley first.
+1 for each of those, and i’ll add clarice starling, uhura, michael burnham, Evelyn Quan Wang (everything everywhere all at once), helen lyle (candyman)