Żyła started jumping at the age of eight and started for the WSS Wisła club . He played his first international competitions in 2003. In the 2004/05 season he was used in several Continental Cups . At the Junior World Championships in 2005 in Rovaniemi , he was able to win a silver medal with the Polish team. In the following summer of 2005 he started in some jumping competitions in the Summer Grand Prix , but could never reach the points. At the beginning of the following winter season 2005/06 he reached mediocre placements in the Continental Cup, but still got a job at the World Cup in Sapporo at the end of January 2006 . With a 19th place, he was able to achieve World Cup points straight away. On February 4, 2006, he was able to win the Continental Cup jumping in Villach . With the exception of fourth place in Iron Mountain , he was only able to achieve placements in the midfield in the remaining Continental Cup season. In the following 2006/07 season, he commuted between the World Cup and the Continental Cup. At the Nordic World Ski Championships 2007 in Sapporo, he was also used. Although he missed the second round in both individual competitions, he was able to achieve fifth place in the team competition with the Polish team. In the summer of 2007 he again took part in the Summer Grand Prix and was able to achieve his first result among the top 10 in a first-class competition with a 7th place in Hakuba . In the 2007/08 winter season he switched back and forth between the World Cup and the Continental Cup, but got a job at the 2008 Ski Flying World Championships in Oberstdorf, where he was able to take tenth place in the individual competition. In summer 2008 he started mainly in the Continental Cup. At the Polish championships on the large hill on February 14, 2009 he jumped third for the first time to a medal rank.
He achieved his first two podium finishes in the first half of 2011 with the Polish team at the team competitions in Willingen and Lahti . On January 9, 2013, he was able to jump on the large hill in his home town of Wisła with sixth place, his best individual result in the World Cup to date.
At the Nordic World Ski Championships in 2013 he and his teammates Maciej Kot , Dawid Kubacki and Kamil Stoch won the bronze medal in the team competition behind Austria and Germany and thus the first Polish team medal in ski jumping at a world championship. In Trondheim Żyła decided the qualification for themselves. A few days later, on March 17, 2013, he celebrated his first World Cup victory when he triumphed together with the Austrian Gregor Schlierenzauer at Holmenkollen in Oslo . On March 22nd, he jumped on the podium for the second time as third in ski flying in Planica .
Żyła was part of the Polish squad for the 2014 Winter Olympics in Sochi and was used there in two of three competitions. In the individual on the large hill he finished 34th and with the Polish team he was fourth. At the Nordic World Ski Championships in Falun in 2015 , he finished 33rd in the individual competitions on the normal hill and ninth on the large hill. In team jumping he won the bronze medal together with Klemens Murańka , Jan Ziobro and Kamil Stoch .
On December 3, 2016, Żyła won the team competition in Klingenthal together with Kamil Stoch, Dawid Kubacki and Maciej Kot . This was the first victory of a Polish team in a World Cup team competition. On January 6, 2017, he was able to jump on the podium for the third time in his career at the Dreikönigsspringen in Bischofshofen . With this placement, he also secured second place in the overall ranking of the Four Hills Tournament 2016/17 behind Kamil Stoch. At the Nordic World Ski Championships 2017 in Lahti , he finished 19th in the individual on the normal hill. In the individual competition on the large hill, he won the bronze medal in third behind Stefan Kraft and Andreas Wellinger . In the team competition he became world champion together with Dawid Kubacki, Maciej Kot and Kamil Stoch ahead of Norway and Austria. In March 2017 he set a new Polish national record in ski flying at Vikersundbakken with a width of 245.5 meters , which was exceeded by Kamil Stoch in Planica that same month . He finished the 2016/17 World Cup season with 634 points in eleventh place in the overall World Cup and thus achieved his best result to date.
At the Ski Flying World Championship 2018 in Oberstdorf he finished 17th in the individual and won the bronze medal in the team competition together with Stefan Hula , Dawid Kubacki and Kamil Stoch. On February 4, 2018, he achieved the fourth individual podium of his career in third place at the World Cup jumping in Willingen . At the 2018 Winter Olympics in Pyeongchang , he was part of the five-man Polish squad. However, it was not used in any of the three competitions. In the overall ranking of the Summer Grand Prix 2018 , he took third place behind the Russian Jewgeni Klimow and the German Karl Geiger , where he competed on August 4, 2018 on the Andreas-Küttel-Schanze in Einsiedeln, Switzerland, together with his compatriot with the same number of points Kamil Stoch could decide for himself. In addition there were the team success in the domestic Wisła and two second places in Wisła and the Romanian Râşnov .
At the 2019 World Championships in Seefeld in Tirol , he finished fourth in the team competition with the Polish men's team. In the individual competitions he took 19th place on the large hill and 33rd place on the normal hill.