Born in Lima in 1976, Llosa did her undergraduate degree in Film Directing and then went on to study for a Masters in Scriptwriting for Film and Television at the TAI School of Arts and Film in Madrid. After specialising in Film Directing at the University of New York, she made her feature-length debut with the film Madeinusa (2006), which took home the Critics' Award at the Rotterdam International Film festival, among other accolades.

Her second film, The Milk of Sorrow (2008), was awarded the Golden Bear in Berlin and an Oscar nomination for Best Foreign Language Film. In 2014, came the release of Aloft, her most ambitious production yet, starring Jennifer Connelly, Cillian Murphy and Mélanie Laurent.