The list of Heroic traits that feature birth, childhood, identity, betrayals, flaws, death and resurrection, and special powers for Aya.

Heroic Traits

Magical/Mysterious Birth
Aya's birth is missing, although seemingly normal. We know that she is half Japanese and half American, but her birth is otherwise missing from the story. It is hard to judge if it were magical or mysterious at all. Being as that it is never stated, I would assume it is normal as far as the standard for being born go.
Missing/Questionable Childhood
Again, much of this is missing. We do know that her sister and mother were in an accident and died as a result. We do know that Aya received an eye transplant after Maya's death and we know that she was in the hospital for a little bit (Tokita 1998). I've been wondering if Aya was also in the accident and doesn't remember it, or if she was merely in the hospital to receive the transplant. Aya was presumably raised by her father although he is rarely if ever mentioned.
Identity in Question
Aya has been a police officer for the New York Police Department, a MIST agent working for a branch of the CTI, and a time traveler. Her identity is solidified as a strong and capable woman. She is unsure in Parasite Eve I because she does not know why or how she came to get the ability to use her mitochondria. She has no idea why she is able to do what she does until late in the game when it is revealed that her sister was the previous Eve (Tokita 1998). Before that Aya fights silently with her being different speculating on why fate chose her for such a task. Aya never questions her identity openly.
Betrayal
Eve betrays Aya, not because she means too. In fact, when Eve reaches out to save Aya from dying at the altar, Eve creates overdrive. In doing so her soul shoots into Aya's body and shatters the older sister's soul. This results in Aya's death anyways and creates the twisted and the highborn which take over New York (Toriyama 2010).
Tragic Flaw
Aya takes on everything herself. If she is the cause of a problem, she handles it. This is true in Parasite Eve II when her DNA is taken and used to create the Artificial Neo–Mitochondrial Creatures. She feels the mission has become personal and becomes determined to stop them. She also decides to take care of her physical clone, Eve. By the end of Parasite Eve II, they are living as sisters (Hirata 1999). In 3rd Birthday when her soul is shattered and she creates the twisted her solution is to die so that they can never be created. Aya would do anything to protect those she loves and because of it, it results in her death (Toriyama 2010).
Death at the Hands of Evil
Aya survives two games with only minor cuts and bruises. In 3rd Birthday she is surprised when her wedding is attacked. Both she and her groom are killed by the military group that stormed the chapel (Toriyama 2010). As Hyde was running the group, I would say this is her death at the hands of evil. That aside, it is this event that leads Eve to create overdrive and inevitably kill her.
Resurrection Myth
In 3rd Birthday we know that both Aya and Kyle are shot and presumably killed. But we see Aya standing there trying to remember what is going on. She survived and we are led to believe that Eve was killed. Aya has somehow lived, or come back to life and is fighting to stop the twisted that resulted from the attack on the church. Eventually we find out that only Aya's body has lived and that Eve is really who we are playing as (Toriyama 2010). With her ability to go back and forth in time, we head back to ground zero to save Aya and Kyle, where we learn the truth of the matter: Eve unknowingly killed Aya. Afterwards, Aya sacrifices herself so that New York and her family can be safe. Eve is allowed to live life as she wants too. In a special scene, there is a young blonde woman who wishes Eve a "Happy Birthday". When Eve turns to see her she barely glimpses what might be Aya (Toriyama 2010). Technically, Aya Brea (the physical body) survives while the spirit moves elsewhere. Being as that Eve is in Aya's body, it is a little bit trickier when it comes to resurrection.
Special Powers
Aya's special powers stem from her superior mitochondria. She is able to harness the energy in her cells for the use of healing, attack and defense. Eve's abilities are the control of the neo–mitochondrial creatures and then later the overdrive ability that 3rd Birthday revolves around. Only these two women can use either of these particular abilities.