Anna began her dance training at the age of 5 at the Yamada Ballet Studioin her hometown. She also trained at the Australian Ballet School in Australia and the Royal Ballet School of Antwerp in Belgium, and attended several summer programs such as American Ballet Theatre and P.A.R.T.S.in Roses, Belgium.
After graduating from the Royal Ballet School of Antwerp, Ishii returned to Japan and joined Tokyo City Ballet where she danced 'Swan Lake', 'Nutcracker', 'Coppelia', 'Romeo and Juliet', 'Giselle', 'Sleeping Beauty', 'Paquita', and 'The Carnival of Animals' among others. She also danced leading roles with choreographers at company. After her 5 years with Tokyo City Ballet, she decided to return to Europe to join the Ballet de Catalunya, where she worked with Remi Wortmeyer and Larissa Lezhnina.
Anna joined the Ballet de Barcelona since its first day and its premiere in June 2019. She has performed 'Le Corsaire Pas de Deux' and debuted as The Sugarplum Fairy in The Nutcracker in December 2019. In January 2020, she will make her debut as choreographer in the new production of the Ballet de Barcelona of 'Peter and the Wolf'.