The Alita: Battle Angel film focuses on Alita's (Rose Salazar) background in a way that the anime never does. In fact, the anime barely touches on the character's background at all. The movie draws several plot elements from later on in the manga — details about Alita's backstory that are woven throughout the film to build us a more complete character. For example, the flashbacks in the movie that show Alita's past life in which she was a Berserker battling in the warzone on Mars don't occur in the anime, but they're an important piece of canon, vital to setting up the discovery of Alita's identity and destiny.
Likewise, the lost martial art of Panzer Kunst that Alita uses to kick every robotic but from here to — uh — robot Timbuktu was taken from the manga, not from the anime. This fictional martial art was used to set up the whole lost identity storyline after Dr. Ido (Christopher Waltz) sees her lay the smack down on a handful of villains.