Bachynska made her international debut at the France Top 12 meet in March 2017. She later competed at the Stella Zakharova Cup, sweeping the junior events.
2018
In 2018, Bachynska was selected to represent the Ukraine at the 2018 Youth Olympics. She qualified in first place to the all-around and floor exercise finals, second on vault, uneven bars, and balance beam. During the all-around final she finished third behind Giorgia Villa of Italy and Amelie Morgan of Great Britain after falling on floor exercise. During event finals Bachynska won bronze on floor exercise, placed fourth on vault and sixth on uneven bars and balance beam. It was later revealed that Bachynska had competed at the Youth Olympic Games with a collarbone injury and was advised by doctors to rest for two months afterwards.
Senior
2019
Bachynska turned senior in 2019 and made her debut at the Ukrainian Championships. She finished second behind Angelina Radivilova. She later competed at the Baku World Cup where she qualified to the uneven bars and balance beam finals. She finished seventh in the uneven bars final and fourth in the balance beam final, incurring a 0.5 penalty for having her coach present on the podium. In April Bachynska competed at the 2019 European Championships where she placed fifth in the all-around and seventh on the balance beam. In June Bachynska competed at the European Games alongside Diana Varinska and Angelina Radivilova, where she qualified to the all-around in fourth place and the floor exercise final in second. During the individual all-around final she suffered mishaps on the uneven bars and the floor exercise and she finished in 14th place. During the floor exercise final she performed cleanly and won gold. After her success at the European Games, Bachynska received an apartment from the mayor of Ternopil. She was also awarded the Order of Princess Olga by the President of Ukraine, Volodymyr Zelensky. In September Bachynska competed at the Paris Challenge Cup where she won silver on balance beam behind Anastasia Agafonova of Russia and placed sixth on uneven bars. In October Bachynska competed at the 2019 World Championships where she finished the all-around with a score of 52.165 and did not qualify to any event finals nor was the Ukraine able to qualify a team to the 2020 Olympic Games. Due to teammate Diana Varinska scoring higher than her, Bachynska was not able to qualify as an individual to the 2020 Olympics either. In November Bachynska competed at the Cottbus World Cup where she placed fifth on balance beam but won gold on floor exercise.
2020
In late January Bachynska was listed on a nominative roster that was released for the Melbourne World Cup, taking place on February 20–22. While there she qualified to the uneven bars and balance beam finals where she placed seventh and third respectively. She later competed at the Baku World Cup; during qualifications she finished seventh on vault, sixth on uneven bars, and third on balance beam and therefore qualified to the event finals. However event finals were canceled due to the COVID-19 pandemic in Azerbaijan.
