Richardson began climbing in 1871 although she did not become well-known until 1879, when she became the first person to traverse Piz Palü in the Bernina Range. In 1882, in a span of eight days she climbed the Zinalrothorn, the Weisshorn, the Matterhorn and Monte Rosa. Accompanied by Pierre Gaspard and J. B. Bich, in 1888 she became the first woman to climb La Meije, which the editor of the "Alpine Journal" at the time thought to be "the most noteworthy" event of the climbing season. The same year, she made the first ascent of the Aiguille de Bionnassay, the first traverse from the Bionnassay to the Dôme du Goûter, and the first ascent of the Aiguilles des Charmoz. In 1889 she made the first traverse from the Petit Dru to the Grand Dru.