I would say that you need some knowledge and skills in extreme sport. For example: diving, climbing/rappelling, skiing, skydiving, parkour,horse back riding, martial arts, good driving skills (for car chases - without hitting innocent people), flying an airplane/helicopter, sailing etc.
So for these abilities it takes a lot of psychical strength, speed, good motor coordination, fitness, agility, balance, and not being afraid of heights, speed and pain.
Mentally you should be able to keep calm in stressful situations and be able to stay on top of things, have good analytical sense, trust your intuition, dare to take risks, be able to ignore pain and shocking events until you have time and space to deal with it, and put your own needs second (don't think of the reward, the honor or your street creditability -those things doesn't matter to a real hero and heroine).
It can be difficult to keep clam in stressful situations, but in those cases it is important to remember why you are doing this, stay focused on the better cause of it, and the difference and good deed you are doing to the people involved and society. This is also why I think it's important to make some "mental workout", like meditating, train your logical thinking, concentration and focus, and learn about psychology. The psychology is important both in terms of understanding your enemies and to understand your own reactions when you've experienced something traumatizing during your heroic actions.
Even though this sound really unheroic-ish, I still think that it's a good advantage for a heroine to be good looking. It might be a cheap trick, but if a handsome look can save you and the victims of any harm it's good. Charm is also a good thing to have and use, but you can't and shouldn’t rely entirely on your looks and charms, there's a big risk that your enemies won't fall for it - they are, after all, psychos.
Also, good looks increases your confidence which is important when dealing with enemies and when standing alone with such big responsibilities and risks - there's not time to be in doubt. It is also expected from the world that a heroine is secure and confident.