Uh, you haven't said you've done anything wrong that requires forgiving.
On the other hand, you've said she :
- tells you that that she likes you (knowing you like her) and then just 1 week later changes her mind. This is incredibly poor behaviour and she should have apologised for it if she cares about you; and
- she is constantly calling you boring. This is a nasty thing to say to a friend, let alone someone she had feelings for.
If you keep going at her, you will lose her. No one has respect for a person who accepts being treated badly and keeps coming back for more, and no one likes being bombarded by someone they don't want to talk to all the time (or at the time).
Personally - I'd go completely the other way and just let her go, and get on with her life. She's done the wrong thing by you; going after her will drive her further away; and you need to do things for your own self-respect - not putting yourself down in the hope that she'll 'wake up' and like you (it just won't happen that way).
Back off. If she does have feelings for you, she'll eventually come back.