It means she struggled to change something about herself, and now she's very happy with the result. Maybe she was afraid to express an opinion, but now she has overcome that fear, and she feels more confident.

Well, she loves her new self/ personality more than she has always been and she worked so hard to be that new version of herself and from the meaning you get the feeling that she turned herself into a new good satisfied strong woman. good and inspiring quote.

"I love the person I've become because I fought to become her" Notice the word because. Very interesting. She is not saying she loves the person that she has become because she is simply better than before. She is saying she loves the person she has become because she fought to do it. So to understand this if she actually changed without 'fighting' wouldn't she be happy with herself I am speechless.

Somebody tried very hard to change and it finally happened so she is very happy now to be who she is.