She didn't want to just beg for their forgiveness. Write something that would earn her pity, the way her life story if written down might seem designed to inspire. But neither did she want to deprive them of the full story. They needed to understand just as much as Layne had to. Without the proper context, they would never be able to give it a place in their own lives. They might not ever be able to; certainly might not ever be able to forgive her. But she had to present them with the option to, at least.
So, she decided to write them *two* letters, with one only to be opened if they should ever feel ready for it.
In the first letter, she told them what she had done and offered her apologies to the best her writing skills allowed. She gave them a basic explanation, acknowledging that it was wholly insufficient. She told them she can not ask for their forgiveness, nor their understanding, but that the second letter tries to explain it all as best she can. And that if they do not want to hear it, they have every right to never read it.
In the second letter, she writes down her lifestory, or at least the parts of it that ended up leading her to this point. She does not draw it out for pity points, but neither does she try to keep herself from writing down the parts that matter: The slaughter of her family by slavers. Then having those same slavers turn her into a tool to capture and hurt more slaves with. Made into an attack dog for their amusement. Being sold into the mines on Kessel when she outlived her usefulness. Forced to fight and kill again to survive. Taken and tortured by the Sith. Killing the Sith only to be turned into one herself and forced to kill even more people. The struggle with it all, both before and after she became a Jedi. Her obsession with redeeming herself; doing what was right for all the wrong reasons. And at last, the way she fooled herself into believing the death of Lt.Ujips was to be a stepping stone to truly earning that redemption she sought, and realizing her terrible mistake only when it was too late.
The letter doesn't try to justify any of it; merely to help them place it all in a context that might one day help them make some sense of it, just as writing it all down now was helping her do the same.

Today was better than yesterday.
Tomorrow might be better still.
She knew it would be a long process that was nowhere near done, and she knew she would likely stumble along the way. She wasn't going to let things turn out the way she'd seen; wasn't going to fall into despair like that by running down the same path again. But neither was she just going to follow the path now laid out for her by others. Maybe that part was just her being stubborn again; but that stubborness hadn't always led her astray. It had made her do some pretty terrible things, but it had made her do the best things she'd done, as well.
Going forward, she was sure she would disappoint people again, from time to time. But she had no intention of doing the same to herself. Or if she was to do so, well, she would find a way to live with it. The path to healing started with acceptance, after all.
She had been many things in her life, and she could never just be any one of them.
Slave. Slaver. Liberator;
Victim. Killer. Hero.
Murderer.
Strong and wise. Weak and foolish.
The center of the storm. Nothing more than a leaf.
It was time to accept that it was all a part of her.