Aldabergenowa started in the 2011/12 season for the first time in the European Cup. She achieved five top 10 placements and took third place in the Aerials discipline ranking. In the World Cup , she made her debut on February 25, 2012 in Minsk and achieved 15th place. At the beginning of the 2012/13 season , she came in tenth place in Changchun for the first time under the top ten in the World Cup. At the season highlight, the 2013 World Championships in Voss , she finished 17th. In March 2013, she won two European Cups in Airolo and, as in the previous year, came third in the aerials discipline. In the 2013/14 season she came in the top ten six times in the European Cup. She achieved 3rd and 1st place in Chiesa in Valmalenco as well as second place in the aerials discipline at the end of the season.
At the 2014 Winter Olympics in Sochi , Aldabergenova finished sixth. In the following season 2014/15 she reached three top 10 placings in the World Cup and at the end of the season 17th place in the Aerials World Cup. At the 2015 World Championships on Kreischberg , she took 18th place. In March 2015 she won the silver medal at the Junior World Championships in Chiesa in Valmalenco. In the same month she also won her fourth European Cup there. After finishing 3 and 2 in the European Cup in Ruka at the beginning of the 2015/16 season, she won three European Cup victories and won the Aerials discipline. In the World Cup she was twice in the top ten. She achieved her first World Cup podium with second place in Moscow and finished 15th in the Aerials World Cup at the end of the season.
In the following season 2016/17 Aldabergenowa won three times in the European Cup and also took third place twice. As in the previous year, she won the aerials discipline ranking. Her best result of the season in the World Cup was ninth in Pyeongchang . At the end of January 2017, she won the bronze medal at the 2017 Winter Universiade in Almaty . At the 2017 World Championships in Sierra Nevada , she jumped to 17th place. In the 2017/18 season , a tenth place in Moscow was her best result in the World Cup, at the 2018 Winter Olympics she reached 13th place. The following year she was ninth in the individual and eighth in the team competition at the World Championships in Park City and won the Winter Universiade in Krasnoyarsk the bronze medal. In the 2019/20 season she achieved three top ten placements, including third place in Almaty, and 15th place in the Aerials World Cup.