She debuted at World Cup on December 1, 2007, in Finnish Kuusamo where she finished 61st in classical sprint. That season, she had three Top-30 results and earned her first World Cup points. As of January 2022, Antsybor's best World Cup individual finish was 19th at a 7.6 km event in Liberec, Czech Republic, on December 16, 2008, and best World Cup team finishes were 11th in team relay in Lahti, Finland, on January 24, 2021 (together with Kaminska, Olekh, and Kovalova), and in Gällivare, Sweden, on November 21, 2010 (together with Nesterenko, Hryhorenko, and Shevchenko).
At the 2010 Winter Olympics in Vancouver, she finished 14th in the 4 × 5 km relay (together with Zavalii, Hryhorenko, and Shevchenko), 15th in the team sprint (together with Hryhorenko), and 37th in the 10 km events. Antsybor also competed in the 7.5 km + 7.5 km double pursuit event, but did not finish.
Antsybor was nominated for Ukrainian national team at the 2018 Winter Olympics in Pyeongchang.[4] She was 46th in 10 km individual race, 53rd in skiathlon, 56th in sprint, and 19th in team sprint (together with Antypenko).