Tudegeschewa appeared internationally for the first time at the 2003 Snowboard World Championships on Kreischberg . There she finished 37th in parallel slalom, 35th in parallel giant slalom and 16th in snowboard cross. She completed her first World Cup in January 2003 in Berchtesgaden , which she finished in 29th and 28th place in snowboard cross. In the 2004/05 season she came sixth in the parallel giant slalom in Maribor for the first time under the top ten in the World Cup. At the Snowboard World Championships 2005 in Whistler she was fourth in the parallel slalom.
In the following year, Tudegeschewa achieved fifth place in the parallel giant slalom in her first Olympic participation and won the gold medal in the parallel giant slalom at the Snowboard Junior World Championships . After placing 23 and 11 at the beginning of the 2006/07 season , she achieved her first podium finish in the World Cup in the parallel giant slalom in St. Vigil and won her first World Cup victory at the following World Cup in the parallel slalom in Bad Gastein . At the season highlight of the 2007 Snowboard World Championships in Arosa , she won the gold medal in the parallel giant slalom. She also achieved fifth place in the parallel slalom. This was followed by three top ten results in the World Cup and at the end of the season 11th place in the overall World Cup and seventh place in the Parallel World Cup. At the 2007 Snowboard Junior World Championships in Bad Gastein, she won silver in the parallel slalom and gold in the parallel giant slalom. In the following season she came in the top ten five times in the World Cup, including two second places and a third place, reaching 19th place in the overall World Cup and 11th place in the Parallel World Cup. Her best World Cup result in the 2008/09 season was fifth in the parallel giant slalom in Sudelfeld . At the Snowboard World Championships 2009 in Gangwon she finished fifth in the parallel giant slalom and won the bronze medal in the parallel slalom. In the 2009/10 season she achieved top ten results in the World Cup. She won the parallel giant slalom in Nendaz and La Molina , and at the end of the season she finished eighth in the overall world cup and fifth in the parallel world cup. At the 2010 Winter Olympics in Vancouver , she was tenth in the parallel giant slalom.
At the beginning of the 2010/11 season , Tudegeschewa won her fourth World Cup victory in the parallel slalom in Landgraaf . In the further course of the season she won the World Cup five times and also achieved second and third place once and thus won the parallel World Cup. At the season highlight of the 2011 Snowboard World Championships in La Molina, she achieved sixth place in the parallel giant slalom and fifth place in the parallel slalom. After finishing second in the parallel slalom in Landgraaf at the beginning of the following season, she came second in Jauerling and third in Sudelfeld. In the parallel giant slalom in Stoneham she won her tenth World Cup and at the end of the season she finished fifth in the Parallel World Cup. In the 2012/13 season she came in eight World Cup competitions, seven times in the top ten, including third place in Moscow and first place in Rogla . At the Snowboard World Championships 2013 in Stoneham , she won the gold medal in the parallel slalom and finished 11th in the parallel giant slalom. She finished the season in fifth place in the Parallel Slalom World Cup and fourth in both the Parallel Giant Slalom World Cup and the Parallel World Cup. At the beginning of the 2013/14 season she was third in the parallel giant slalom and second in the parallel slalom in Carezza . This was followed by three top ten placements and at the end of the season sixth place in the parallel giant slalom world cup, fourth place in the parallel world cup and third place in the parallel slalom world cup. At the season highlight, the 2014 Winter Olympics in Sochi , she finished 16th in the parallel slalom and 15th in the parallel giant slalom.
In the following season Tudegeschewa reached her only top ten placement in the World Cup with eighth place in the parallel slalom in Bad Gastein. At the 2015 Snowboard World Championships on Kreischberg, she came ninth in the parallel giant slalom and eighth in the parallel slalom. After third place in the parallel giant slalom in Carezza at the beginning of the 2015/16 season , she won her 12th World Cup victory in the parallel slalom in Bad Gastein and came third in the parallel giant slalom in Rogla. At the end of the season, she finished second in the Parallel World Cup, the Parallel Giant Slalom World Cup and the Parallel Slalom World Cup. In the 2016/17 season, with five top ten placements, she reached 13th place in the Parallel Slalom World Cup, 11th place in the Parallel World Cup and ninth place in the Parallel Giant Slalom World Cup. At the season highlight of the Snowboard World Championships 2017 in Sierra Nevada , she won the bronze medal in the parallel giant slalom and finished 11th in the parallel slalom.
In the 2017/18 season Tudegeschewa came in 12 World Cup starts, ten times in the top ten. In January 2018 she finished second behind the German Ramona Theresia Hofmeister at the parallel slalom in Bad Gastein. At the highlight of the season, the 2018 Winter Olympics in Pyeongchang , she finished 14th in the parallel giant slalom. At the end of the season she won the Parallel Slalom World Cup and came in sixth in the Parallel Giant Slalom World Cup and fifth in the Parallel World Cup.
Tudegeschewa became Russian champion in snowboard cross (2003, 2004, 2006), parallel slalom (2007, 2012, 2016) and parallel giant slalom (2005, 2007, 2012, 2016).