Ambiguous Disorder: After spending many years isolated away from people and locked in a castle, Anna displays hyperactive behavior such as extreme restlessness, an inability to sit still for too long, a serious case of racing thoughts along with Motor Mouth, and impulsive and reckless behavior.
Even when believing that her aloof older sister didn't love her because Elsa shut her out and became closed-off toward her, and when Elsa shoots ice spikes at her and then covers the kingdom with an Endless Winter, Anna never gives up her belief in Elsa's goodness and risks her life as she struggles through a blizzard to prove it, rather than letting people's fear of the queen prevail and taking the kingdom for herself like Hans later attempts to do.
All-Loving Heroine: All she wants is to reconnect with her big sister, and she believes in The Power of Love.
Ain't Too Proud to Beg: When Hans attempts to advance the icy curse Elsa accidentally placed on her by putting out everything that is fire lit, she is reduced to begging.
Agony of the Feet: She gets hers stepped on by the Duke of Weselton while they dance.
Age Lift: Gerda in The Snow Queen is a young child, while Anna is eighteen for most of the first film, which is the one most strongly based on the tale.
Adaptational Name Change: Her counterpart in the Andersen tale is called "Gerda".
Adaptational Badass: Gerda, on whom she is based, is more of an Action Survivor while Anna is an Action Girl.
Despite her lack of powers, she still climbs her way out of a cave, leaps from one cliff edge to another, confronts a group of rock giants and gets them to destroy a dam she lures them to by standing on it so they'd throw boulders at it before leaping away when it starts to crumble. Elsa still ends up leaving her behind, but though never involved in direct combat Anna more than proves her bravery by the end of the film. Elsa insists that Anna would be in danger following her, which leads Anna to list some of her badass credentials from the first movie. In the end, she punches Hans in the face with enough force to knock him off a ship.
In the first film, she holds her own when helping Kristoff fight off the wolves, bludgeoning one of them with Kristoff's lute and then burning Kristoff's bedroll and throwing it to stop another one in its tracks.
Written to be a realistic hero, she can hold her own, but doesn't always rely on that. Anna may be a normal human without any magical powers like her sister Elsa, but that doesn't make her any less fearless and capable of being badass.