Tjunkaya grew up at the Ernabella Mission where she went to school and later worked learning and demonstrating to her peers various domestic skills including sewing, cooking, and house cleaning, using European equipment and methods. In mission days, the building which is now the art centre was originally used as a food hall by the missionaries. In 1948 it became the Craft Room, where the first work was by women, spinning wool and rug making. Most of the senior artists painting on the APY Lands today have passed through this building across more than one of its incarnations.
Tjunkaya began work in the craft room in the medium of batik, and became one of the outstanding artists with work in several public collections. Her work was featured on the cover of Judith Ryan's 'Across the Desert: Aboriginal Batik from Central Australia.'
Tjunkaya also works in ceramics, tjanpi, punu, print making, spinning and mukata making and her work in these mediums has been seen in numerous exhibitions in Australia and internationally since 1971, in public and private galleries.
Over the last three years, Tjunkaya has chosen to concentrate exclusively on painting and tjanpi sculpture. This focus has seen her become one of the most in demand female artists on the APY Lands and increasingly recognised in these two mediums. In 2010 and 2011 she was collected by Artbank, and in 2011 and 2012 selected as a finalist in the Togart Contemporary Art Award. In 2012 her tjulpu (bird) tjanpi sculptures were selected for exhibition in the National Aboriginal and Torres Strait Islander Art Awards (the Telstras). 2011 marked the commencement of Tjunkaya's 5th decade of working at Ernabella Arts. In 2020 Tjunkaya was awarded an Order of Australia (OAM) in honour for her work in education and art.