I am trying to remember the name of a horror film 2002-4 about woman with amnesia who is overcoming her parents being murdered and tutor murders start occur help?

You're likely thinking of "The Hunted" (2003), starring Halle Berry.

Here's why it matches your description:

* Amnesia: The protagonist, a skilled assassin, suffers from amnesia after a traumatic event.

* Parents' Murder: She's haunted by the murders of her parents and struggles to recover from the tragedy.

* Tutor Murders: She's being hunted by a shadowy figure who was responsible for the murders.

Let me know if this is the movie you were looking for!