There are many heroic acts in this movie — as there were in the real life events it’s based on.
The real shift, however, is when Ben Bradlee realizes (thanks to a little coaching from his wife), that the water he’s swimming, despite all of his desperation, may not be as choppy as the water Katharine Graham is swimming in.
In other words, everything shifts when he considers what she has at stake — beyond the dollars or even the first amendment. This understanding of one human being for another is what propels the story forward to its liberating conclusion.