Well, you're more familiar with X than
me, therefore you tell me if I'm wrong.

It seems to me that Kotori is killed and
then does try desperately to prevent her
brother to kill Kamui.

If it is the case, she does not sacrifice
anything, since already dying (she does not
choose to do some self-sacrifice herself. She is
sacrificed/killed and then decide to do something,
having nothing to loose or to do anyway)

Well, I am not sure if I am not totally
re-imagining the story here, you've got me
confused... I may have to re read/view that
part again...