How can you write a good female character that isn't just an "idealized version of herself" or her author's ideals of what women are like?

Give her a strong personality with strong opinions. Give her faults and flaws. Have her display ignorance, misunderstand things, get things wrong, and then show her evolve and learn.

A “good” character is a relatable one who has an interesting arc. If either female or male characters represent the author’s ideal, they’re not going to be very interesting. They sure can be used to show the author’s ideals, or can evolve to be closer to the ideal, but if they start out perfect where do they have to go?

For a long time female characters seldom had much character. They were damsels in distress, supportive mothers, “fridged” girlfriends to provide motivation for the male hero. Somewhere around the 80s or 90s the pendulum swung a bit too far the other way and all women were smart, tough, no-nonsense, independent badasses… who were still usually secondary characters and far too often fell for the hero in the end anyway. I love Ellen Ripley, a badass lead who didn’t have a forced romance, but I don’t want every character to be Ellen Ripley. I think too this fed the horrible “not like other girls” trend that’s only a repackaging of misogyny.

A character can be smart and independent and still be interesting; she can also be in over her head and helpless and still be interesting. She just needs a distinct, compelling personality and an arc, that’s what makes a strong character. Some tips:

Try to give her a goal that is NOT about a man. She can fall in love, but her story shouldn’t be only a quest for a husband. She can have a strong connection to her father, but don’t use the “I learned martial arts because daddy wanted me strong” cliche. She should want and do things for herself.

Give her actual flaws. “Clumsy,” “bad cook,” or “can’t sing” aren’t flaws. Make her whiny, make her prejudiced, make her overconfident, something that’s an actual problem to overcome.

Have her screw up. This is halfway between the bullet above and the one below. Someone who’s always right isn’t relatable because we’re all flawed people who screw up. She can even do mean or downright bad things: women aren’t delicate angels. We fuck up, we hurt people (sometimes even on purpose), we self-sabotage.

Make her relatable. This is where a lot of authors fall down because they don’t understand what that means. She has to have characteristics and goals that a typical woman (yes, a hard thing to define) can look at and say “I get that!” It’s nice if you can skip that cliche “standing up to a misogynistic authority figure” thing. Maybe there’s something she wants to learn, or win, maybe she wants to make friends, or be more confident, or save a family member, or explore a new place, or fight against oppression. All those things will resonate with a lot of people.

Please don’t make her “not like other girls.” Give her some non-romantic relationships, including with other women. Let her respect some women and hate others, that’s realistic.

One of the most interesting female characters I’d read in a long time was the protagonist of Convenience Store Woman. She’s antisocial and probably somewhere on the autism spectrum, relationships don’t make sense to her, and while she struggles for a while to conform she ends up embracing what actually makes her happy. That was really unique! On the other hand, I like Lizzy from Pride & Prejudice, too. In a time when finding a husband was the only thing, she was open to romance but more interested in observing society and supporting her favorite sister. And I feel for Wendy Torrence from The Shining and Nancy from Oliver Twist; true, their problems stem largely from their romantic relationships but they feel like real people (and defied their abusive partners in the end). These are all radically different women, but I cared about their journeys, that’s the key. Particularly poor Nancy is not at all my vision of an idealized woman, but she had character and trauma and tried to do the right things as much as she could. Your readers need to CARE about the character.