What is it that makes Ántonia a genuinely heroic figure? In what ways does she improvise happiness and emerge successfully from the same circumstances that killed her father?
The “heroic” aspect of Antonia is her intelligence and sense of independence. I think it is problematic to think of her as a “hero” in the classic sense, however. The second half of your question, about Mr Shimerda, might help us understand why this is so. Mr Shimerda kills himself out of despair and depression. He was a skilled musician in Europe, but in Nebraska, he is simply an old man who cannot work and cannot speak the language. In a way, it is his past that defeats him: unable (or unwilling) to forget his past, he fails to embrace his new country.
Antonia is a contrast in that she is unburdened by any such memory. Her heroism is in part derived from her ability to adapt to her new surroundings and make them her own. Her friendship with Jim is a case in point: Jim is attracted to her because of her individualism and her fun-loving spirit. She comes to represent for Jim the spirit of the land; certainly she is, by the end of the novel, a symbol of his youth and proof that the connection to the land they shared as children endures. In that sense, she is, for Jim, a kind of hero.
I would be careful, however, in assigning similar feelings to Cather. One reason I hesitate to call Antonia a hero is that it undermines or simplifies her individuality. One of the curiosities of this novel, written by a woman but told by a male narrator, is that Antonia’s internal life is mostly missing. I think the challenge of the book is, in fact, to resist the temptation to make Antonia into a heroic figure and think instead about her actual life as a woman.
Antonia Shimerda's heroism resides in her ability, throughout the novel, to "keep on keeping on" as they say, despite a life journey through much happiness, including, but not limited to her lack of education, pregnancy out of wedlock, her father's suicide, a lifelong state of poverty. When Jim returns to see her at her family's farm, he is reluctant to go because of this poverty; he fears that his happy memories of the happy-go-lucky Antonia, the one who chose dancing over steady work when they were young, will be sullied by what he assumes will be a poor and pitiful existence. He finds out, however, that he couldn't be more wrong. Antonia has married a kind, loving, hardworking man, a Bohemian like herself, and they have raised up a large family of kind, hard-working, polite children. Antonia's farm is beautiful, just like her family. Her heroism, then, lies a great deal in her spirit, one that never left her, and her intelligence, which led her to internalize the lessons of her life in a way that facilitated her ability successfully manage a home and raise children. Indeed, while Antonia never received the formal education her father so desperately wanted for her, she received a life's worth of education that resulted in wisdom, and a successful conclusion to her "hero's journey"--not monetary success, but success in the area of life that might be argued to be most important, that of one's family.