Tviberg took part in an FIS race for the first time in November 2009 and shortly afterwards made her debut in the European Cup in Kvitfjell , where she finished 61st, however, clearly outside the points. A year later she won her first FIS race with a slalom in Geilo and in January 2011 became Norwegian junior champion in downhill and super G. In the same winter, Tviberg took part in a junior world championship in Crans-Montana for the first time , where she achieved the best result in the downhill took 26th place.
Since the 2012/2013 season , Tviberg has regularly competed in the European Cup. There she was able to score for the first time on December 1, 2012 with 21st place in the Super Combined by Kvitfjell and on December 12, 2012 in the downhill from St. Moritz she achieved her best result to date, which she achieved on January 17, 2013 in the Departure from St. Anton equalized. At the Junior World Championships in 2013 , she won the silver medal in combination behind her teammate Ragnhild Mowinckel . At the end of the season, she became the Norwegian downhill champion. At the beginning of the following winter , she improved her best performance in the European Cup when she finished fourth in the downhill from St. Moritz on December 17, 2013. A day later she reached the same place - also in the downhill - in second place, her first podium in the European Cup. Almost a month later, on January 16, 2014, she won her first race in this racing series with the descent in Innerkrems . At the end of the season, she finished first in the super combination classification and second in the downhill classification.
On January 24, 2015, Tviberg made his debut in the World Cup on the downhill run in St. Moritz and scored her first World Cup points straight away as 16th. At the 2015 World Junior Championships in Hafjell , she won the downhill silver medal. At the end of the season, at the Norwegian Championships in Hemsedal, she won the gold medal in the giant slalom, silver in the downhill and Super G and bronze in the alpine combination. After she was unable to contest competitions due to injury in 2015/16, she has been back in the World Cup regularly since December 2016 and achieved her best ever World Cup result on February 26, 2017 as tenth in the Crans-Montana combination. In the first training session for the Downhill in Lake Louise on November 29, 2017, Tviberg suffered a ruptured cruciate ligament and was then canceled for the entire season.