She has won one silver, one bronze and six Olympic gold medals, three of which in Rio de Janeiro in 2016, making her the first female to win K1, K2 and K4 at the same Olympics (a record equalled in 2024 by Dame Lisa Carrington).

She won a silver medal in the K-4 500 m event at the 2008 Summer Olympics in Beijing.

Kozák then won a gold medal at the London Olympics in the Kayak Four (K4) 500m team event with Gabriella Szabó, Katalin Kovács and Krisztina Fazekas Zur for Hungary.

[3] The latter results made her the most successful Hungarian sprint canoer and the only female athlete to win K1, K2 and K4 at the same Olympics.

Kozák has also won eighteen medals at the ICF Canoe Sprint World Championships with fourteen golds (K-1 500 m: 2013, 2014, 2018; K-2 200 m: 2011; K-2 500 m: 2009, 2010, 2015, 2018; K-4 500 m: 2009, 2011, 2013, 2014, 2018 and K-1 200 m relay: 2013), two silvers (K-1 500 m: 2011 and K-4 500 m: 2015) and two bronzes (K-1 500 m: 2019, K-2 1000 m: 2007).