GRAN MASTER - UKRAINE
Muzychuk's parents, both professional chess coaches, taught her to play at the age of two. She played her first tournament at age five and in that same year she finished second in the under 10 girls championship of Lviv Oblast.
From 1997 to 2005 she won several medals at Ukrainian, European and World Youth Championships. She won gold in the European Under-10 girls championship in 1998 and 2000, Ukrainian under-10 girls championship in 2000, Ukrainian and European under-12 girls championships of 2002, European Under-14 girls championship in 2003 and 2004, World U16 girls championship in 2005. She took silver at the European Under-10 girls championship in 1997 and 1999, European Under-12 girls championship in 2001, World Under-12 girls championship in 2002 and World U14 girls championship in 2004. She was the bronze medalist in the World Under-10 Girls Championship in 2000.
She was awarded the titles of Woman FIDE Master in 2001 and Woman International Master in 2002.
In 2003, Muzychuk also won the Ukrainian Women's Championship. She won the Ukrainian U20 girls championship of 2004.
In 2004, Muzychuk started to play for Slovenia: she was offered a contract by the Slovenian chess federation and was supported by them over the course of the next ten years. She played for the club from Ljubljana and for the Olympiad Slovenian national team. She represented them first in junior and then in adult tournaments, becoming the strongest female chess player in Slovenia and the third best female player in the world. Muzychuk continued to play for Slovenia even when while she lived in Stryi (Ukraine), and her younger sister Mariya, twice represented the Ukrainian national team.
In 2007, she won the European women's blitz chess championship and finished second in the European women's rapid chess championship, both held in Predeal, Romania.
Muzychuk was awarded the titles of International Master in 2007 and Grandmaster in 2012.
In 2010, she played in the Corus chess tournament Group B, finishing 10th with a score of 5½/13 and a performance of 2583. In the same year, Muzychuk won the World Junior Girls Championship in Chotowa, Poland.
She won the bronze medal in the Women's European Individual Chess Championship of 2012. In the same year Muzychuk took part in the ACP Golden Classic in Amsterdam along with Vassily Ivanchuk, Gata Kamsky, Emil Sutovsky, Le Quang Liem, Krishnan Sasikiran and Baadur Jobava. It was a round-robin tournament in which the rate of play was two hours and half for forty moves followed in case by adjournment. She finished fourth with a score of 3/6 and a rating performance of 2721.
Muzychuk finished fourth in the 2014 Tata Steel Challengers tournament, scoring 8/13 (+4=8-1). In April 2014 Muzychuk won the Women's World Blitz Championship. In May 2014, she returned to the Ukrainian chess federation. Muzychuk won the 2014 Ukrainian women's championship in Lviv. In January 2016, she won the women's first prize at the Masters tournament of the Tradewise Gibraltar Chess Festival.
In December 2016, in Doha, she won the Women's World Rapid Championship, and two days later she defended her Women's Blitz World Championship title.
In October 2017, she won the ACP European Women's Rapid Championship in Monte Carlo. In November 2017 she announced she would boycott the 2017 Women's World Speed Chess Championship, to be held in Saudi Arabia, due to Saudi Arabia's rules regarding women. On her Facebook page she commented:
In a few days I am going to lose two World Champion titles – one by one. Just because I decided not to go to Saudi Arabia. Not to play by someone's rules, not to wear abaya, not to be accompanied getting outside, and altogether not to feel myself a secondary creature.