I would first say that Nora, from Ibsen's play A Doll's House, would be a hard character to define as a tragic hero. Tragic heroes, by definition, are characterized very specifically. Based upon the characteristics which align with the tragic hero, Nora only aligns with two: audience must feel fear and pity for the character and the character possess a tragic flaw. Nora is not of noble birth, fails to reverse her fortune, and has not really discovered her own fate (because of her tragic flaw).
As for Nora's tragic flaw, she fails to see reality for what it truly is. Nora refuses to accept the fact that life is not a walk through the roses. When blackmailed by Krogstad, Nora backs into a corner. Instead of facing the truth, initially, about the loan, she continues to lie about the finances of the household. Above all else, Nora lies. She lies about the little things (like the macaroons) and the big things (the forged loan).