Eleftheriou was born in Limassol. In 2006, she won the skeet shooting gold medal at the Melbourne Commonwealth Games. She has also won silver at the 2006 ISSF World Cup in Germany, gold at the 2007 World Cup in Belgrade, Gold at the 2008 World Cup final in Minsk, and placed seventh in the 2008 Olympic Games in Beijing. She won a bronze medal at the 2014 Commonwealth Games in the skeet event and a gold medal at the 2018 Commonwealth Games in the skeet event. She is openly lesbian.