What are some examples of the mother's past behavior in the story "The Leap"?

That's an interesting question. Most of the mother's actions in the story are in the past. The main ones in the present show her in her old age, with her eyesight fading. Almost all the rest of the story is set in the past.
Some of these past behaviors define both the mother and the narrator (her daughter). For example, when the mother was half of "the Flying Avalons," the trapeze act, she engaged in two striking behaviors repeatedly. First, of course, is the fact that she was enough of a daredevil to be in a trapeze act at all. She was willing to risk her life for her profession (or art). Second, she and her partner "laughed and flirted openly" as they did their act. This indicates a willingness to display affection in public, and a kind of showmanship.
Another behavior, very different, can be seen when the mother rescues the narrator from a fire. She is bold and daring, and leaps from a tree to the gutter of the house. She's like a superhero, except that her tap on her daughter's window is tentative and quiet. That's very striking.