Kuschnir made his debut in the World Cup on January 11, 2004 and reached 24th place in Mont-Tremblant . Due to injury, he had to pause almost the entire 2004/05 season and was only able to participate in the national championships at the end of March 2005. He finished the 2005/06 World Cup season with three placements in the top ten, including a fifth place as the best result. At the 2006 Winter Olympics, he finished eighth. The 2006/07 World Cup season was extremely unbalanced : On January 12, 2007, Kuschnir jumped to second place in Deer Valley and thus achieved his first podium, but otherwise he did not get beyond 15th place.
Kuschnir made his breakthrough to the top of the world in the 2007/08 season , with three second places and his first World Cup victory on February 17, 2008 in Inawashiro . In the following season 2008/09 he could not quite hold this level; it resulted in a second place in a World Cup competition and sixth place at the 2009 World Championships in Inawashiro. Kuschnir was far more successful in the 2009/10 season : with four wins, a second and a third place, he won the discipline rankings ahead of time, as did the overall World Cup. Because of his superiority, he was considered the biggest favorite to win the 2010 Winter Olympics . However, he could not withstand the pressure and was eliminated in the qualification round, which ultimately resulted in 15th place.
In the 2010/11 season , Kuschnir won three more World Cup wins and a third place. At the 2011 World Championships in Deer Valley, he won the bronze medal. After he managed to finish third in the 2011/12 World Cup season, he did not compete in the 2012/13 season. He made his comeback in mid-December 2013 and won the World Cup competition in Deer Valley a month later. He celebrated the greatest success of his career at the 2014 Winter Olympics in Sochi by winning the gold medal. In the following two winters, Kuschnir did not contest a single competition. When he intervened again in mid-December 2016, he immediately won the World Cup competition in Beida Lake. In the further course of the 2016/17 season , he was able to record two more World Cup victories.
Kuschnir won a competition in Moscow in the 2017/18 World Cup season , plus a second and two third places. As in the two previous winters, this was again enough for third place in the Aerials discipline ranking. He achieved the same placement in the 2018/19 World Cup season , for the fourth time in a row.