"Beneath every strong, independent woman lies a broken little girl who had to learn how to get back up and never depend on anyone" suggests that behind the confident exterior of a strong and independent woman, there may have been moments of vulnerability and hardship in her past.
The phrase implies that this woman has faced difficulties or experiences that have left emotional scars.
However, she has learned to overcome her challenges and become self-reliant, determined not to rely on others for her happiness or success.