Born in Rælingen in Akershus county,[1] Kristoffersen made his World Cup debut in March 2012 in Kranjska Gora, Slovenia, and attained his first podium in November 2013, a third-place finish in slalom at Levi, Finland.

[3][5] Kristoffersen is the first to win the three classic slalom races in Adelboden, Wengen, and Kitzbühel in the same season; accomplished at age 21 in January 2016.

With his seventh win at Wengen, Kristoffersen tied Finn Christian Jagge, and the eighth came a week later in Kitzbühel to set the record.

At the World Championships in 2019, Kristoffersen won the gold medal in the giant slalom at Åre, Sweden.

Kristoffersen is the first to win the four classic slalom races (of Adelboden, Wengen, Kitzbühel, and Schladming) in a single season.