Annamari Chundak made her World Cup debut in October 2006. Until 2010 Winter Olympics, she managed to qualify for the knockout stage only once – on 6 February 2010, in German Sudelfeld, where she was 14th. She competed at the 2007 European Youth Olympic Winter Festival in Spanish Jaca, where she was 4th in giant slalom and 6th in parallel giant slalom.
In February 2019, she ranked 6th in the parallel giant slalom event at the World Championships which was the best ever result for Ukraine at snowboarding competitions of the highest level. But the next day, she surprised everybody by winning a silver medal in parallel slalom, which was the first-ever medal for Ukraine at international snowboard competitions of the highest level. She was just 15th in the qualifying round after finishing 21st on the blue course and 8th on the red course. In the first round, she won against #2 of the qualification Cheyenne Loch from Germany. Later on, Dancha won against Polish Aleksandra Król and 2018 Winter Olympics bronze medalist German Ramona Theresia Hofmeister. In the final, she lost to Julie Zogg from Switzerland, thus winning the silver medal.[7] Interesting fact that these athletes met each other in the final for the second time. Nine years ago, Dancha (Chundak back then) won against Zogg in the final of the parallel giant slalom at the Junior World Championships.
As of January 2022, her best World Cup finish was 5th in the parallel giant slalom on January 11, 2020, in Swiss Scuol.