When the option of running -- in a fight of flight situation -- is over, what do you do? Freeze up in the moment or prepare for battle. Depending on what you choose, can be a life altering situation, and with those kind of stakes, actions speak louder than words.
The most recent instance of this kind of scenario is Shingeki no Kyojin, with the back story of Ackerman Mikasa in episode six. Because of said back story, we now know why Mikasa is so protective of Eren -- beside him being her only family left -- Eren gave her something to fight and live for; she now had a reason to become stronger, and actually achieve it in the present -- quite evident with how kick ass she is now.
Losing Everything
It is very likely that a character has to lose everything -- or at the very least, the majority of things they hold dear -- to turn colder and flip the switch, in order to do what they need to survive. As I said previously, we see this in Mikasa, when her parents were kill right in front of her, we see the breaking of her character. However, it took Eren killing two of the three murderers -- and him being in trouble of with the third -- to make Mikasa finally do what she had to, to become strong and survive.
Another example is Eren/Elen -- not to be confused with the one from Attack on Titan -- and Reiji, from Phantom. However, I want to focus on Elen, because both her and Mikasa are female characters that went through hell to get to where they are, and I want to continue to be consistent.
Elen didn't have an memories of her past, because of Scythe brainwashing her to become a tool for killing. Since she had nothing to live for in the first place, she had to attach to something for her to keep living, and that was Scythe -- her master -- and the orders he gave to Elen. Through that, she became the best assassin in the world, nicknamed Phantom, and she -- like Mikasa -- were physically strong, because they needed to be for the sake of who they were indebted to.
Not Strong Enough
Although both were physically strong, their psyche wasn't as resilient. They ended up with an imbalance of brawny body, tuned for killing -- or just badly hurting -- those who got in their way, and a very fragile mental state. And they just end up acting stronger than they really were, in order to do what was required, to make them feel like they were living.
However, removing the crutch they had on life -- whether is if Eren, from Attack on Titan, or Scythe -- they lost that purpose that was given to them, and probably would just end up giving up. Fighting without a purpose isn't their style, so these requirement are a must for both females to feel like that can keep moving.
Defeat
These kinds of characters -- like Mikasa and Elen -- are a lot weaker than most characters think. If you simply knock the crutch that is holding them up, they will fall straight to the ground, and probably not get back up.
I don't know what it is, but I really do like these kinds of strong-weak female characters, where they are strong physically, but weak mentally, or even vice-versa. It exposes the fact that characters are not perfect and probably never will be perfect, making them way more believable and interesting.