Is this woman a detective? A foreign agent? FBI? Is she entangled in a global cabal? What if she's not the hero? What if the person on the other side of the gun is the hero?
Here's a fun way to do this exercise: Without deciding who's the hero and who's the villain, write two different scenes. Write the first scene from the head, heart, and gut of the woman with the gun. The other character can only speak and act. Then turn it around and write from the point of view of the character at the other end of the gun! The story can be very different, and you will learn a lot.
Although plot may seem more important the character in a thriller, the truth is they're both important. While we all love a page-turner, it's the characters whom we most remember. The way to develop strong characters and a strong plot is to become an expert in point of view!