I get worried when I see the word strong followed, with or without independent, by female character(s). I think it bespeaks a fundamental misunderstanding of how characterisation works. I feel this is required reading for anyone who wants to understand how to write female characters well - that's the operative word. Here's the key observation:
I think the major problem here is that women were clamoring for
“strong female characters,” and male writers misunderstood. They
thought the feminists meant [Strong Female] Characters. The feminists
meant [Strong Characters], Female.
So feminists shouldn’t have said “we want more strong female
characters.” We should have said “we want more WEAK female
characters.” Not “weak” meaning “Damsel in Distress.” “Weak” meaning
And then the author, Shana Mlawski, herself a YA novelist, finishes with some examples of (SCs) F that work and why.
(See also this webcomic, discussed here.)
Our job as writers is not so much to look up which human traits are "strong" and bundle them onto your characters; it's to make sure the characterisation itself, including character development*, is competent. Can I believe a real human would have this bundle of virtues and vices, given where they came from and what they've been through? Does it make me want to root for them (or against, if they're the antagonist)? Can I believe, given all that they are, what they end up doing?
* When it comes to character development, there are at least three viable "arcs"; just see what works for you.
The last two novels I finished writing each have a 10-year-old female protagonist, but apart from both being smart they've got very little in common. One of them is so good at manipulating others she feels a conflict in herself, fighting not to do anything too evil. It's not a fight she always wins. (I don't blame her, given occasional but serious reasons the world has given her to turn angry.) The other is a continually downtrodden child who starts to benefit from others' kindness, but feels so guilty about not taking the reins much herself that, when she does have only-she-can-fix-it situations, she's willing to do increasingly brave things as part of them, eventually risking her own life.
Attempts to make a female character strong and unique
aren't likely to be unique. It's just an archetype now. Doctor Who marketing often acts as if it's something new that a female companion is like that. It's not unique at all. The first episode of new Who saw Rose Tyler solve a problem by swinging from a cable. And frankly, her successors aren't even following in her footsteps; they're following in those of practically every companion, regardless of gender, the Doctor has ever had.
I want them to be strong, independent, unique girls, without straying into "not like other girls!!!" territory. I don't want them to be copy/paste characters, predictable in nature, or an acre of water an inch deep, per se. How do I keep my characters unique and avoid this trope?
Every person, real or fictional, is somewhere on a bell curve for intelligence, somewhere else for physical strength, somewhere else again for her opinion on politics, or fashion, or whatever. The challenge in characterisation is to think about who they are from every angle one can see the story having to look at.