[1] Muzychuk has experienced multiple successes with Ukraine at the Women's Chess Olympiad winning gold in 2022, silver in 2018 and bronze in 2012, 2014 and 2016.

[9] She made it to the top-16 of the 2010 Women's World Chess Championship, but lost to Dronavalli Harika in an armageddon playoff after a tie in the regular match.

In round three, she defeated former Women's World Chess Champion Antoaneta Stefanova in the classical games by a score of 1½–½.

As a result of her victory, she obtained the Grandmaster title and qualified for the 2015 Chess World Cup which was held in Baku, Azerbaijan.

In 2017 she refused to play in the Women's World Chess Championship 2017 in Iran out of protest for being obligated to wear a hijab.