Good question.? A single adjective is preferable for the sake of brevity.? My 1st inclination was to describe her as merely stubborn. That is certainly her defining characteristic and in most situations stubbornness is a virtue.? Which would be good enough for the logline for the 1969 version.

Long answer:

But the 2010 Coen brothers version has a mixed out come for the protagonist, Mattie Ross, and so I am inclined to think the logline should suggest a character flaw that leads to that mixed outcome.

I am true believer in? the ancient Greek concept of hubris, a? notion that infused and? determined the outcome of (most) Greek tragedies.? Simply stated, hubris is the dramatic “sin”? of excess, of a life , situation or value system that is out of balance.? (In contrast to the Greek ideal of?sophrosyn?,? moderation, restraint.)? The Greeks believed that any virtue carried too far becomes a vice.? It becomes the problem, not the solution.

So in that regard, I would say that Mattie suffers from the an hubris of inflexible stubbornness.? Initially, it’s a virtue in enlisting the services of the U.S. Marshal.? ?But, she doesn’t know when to let up, to let go, to adapt her plan? to the goals of her rival, the Texas Ranger.? She wants the murderer brought to justice her way. Period.? And, so her virtue becomes a vice, a problem that leads to the mixed denouement.

As I watched that ending to the 2nd movie, I imagined the great Greek tragedian, Sophocles (who wrote Oedipus Rex), nodding his head and?whispering (in ancient Greek), “Yeah, the Coen brothers got it right. That’s true dramatic justice.”

But Hollywood movie makers aren’t big on that kind of dramatic justice.? But if you’re the Coen brothers, you can get away with that kind of denouement.

Short answer:

Stubborn is good enough.? But then how to describe the Marshal?? He’s a mixed-bag character.? What makes him such an interesting character is not that he’s tough (his defining characteristic), but that he’s also a drunk.? So if I have the luxury to describe him as “tough, drunken” why not elaborate with one more word for her?

So I did.

fwiw

My version:

A stubborn, revengeful farm girl hires a tough, drunken U.S. Marshal to track down her father’s murderer in Indian territory.
(19 words)

I don’t see the need to lead off with an explicit inciting incident.? It’s implicit in that the characterization of who she’s hunting down: her father’s murderer.? (And to make explicit what is clearly implicit lengthens the logline.)

“Stubborn, revengeful”? is the character flaw that leads her to getting her man — but losing her arm.? (The? 1969 version starring John Way goes for a happy ending for the protagonist.? The Coen Brothers remake is faithful to the book.? How the Coen Brothers foreshadow the consequences of her flaw in the 1st Act and pay it off in the 3rd Act? is well worth studying.)