In 'Brave', the princess who is a skilled archer is Merida.
Merida is Pixar's red-haired heroine and the 16-year-old daughter of King Fergus and Queen Elinor of DunBroch, a fictional medieval kingdom in Scotland. She resists the expectation that she should marry for political reasons and instead insists on choosing her own future.
Archery is central to her character. Merida uses her bow in the film's opening hunt and later enters the clan games herself, challenging the suitors who are competing for her hand. Her athletic abilities also include sword fighting, spear throwing, and riding her horse, Angus.
Mulan, Rapunzel, and Elsa are unrelated Disney heroines from different films. Merida is sometimes grouped with Disney Princess characters, but 'Brave' is a Pixar production. The story turns on Merida's conflict with her mother and the consequences of a spell that transforms Elinor, making reconciliation and family bonds as important as adventure.