[4] In 2013, Boschung competed in ADAC Formel Masters with Team KUG Motorsport[5] and ended the season seventh, having inherited a win at the Slovakiaring after the original race winner and that year's champion, Alessio Picariello, was given a penalty.

In 2015, Boschung debuted in the GP3 Series with Jenzer Motorsport, partnering Pål Varhaug and fellow Swiss Mathéo Tuscher.

However, after the pair of races at the Hockenheimring, where the Swiss driver didn’t score any points,[20] he was replaced for the round at Spa-Francorchamps by Niko Kari, with the team citing financial reasons.

In March 2017 Boschung signed for Campos Racing to compete in the inaugural FIA Formula 2 Championship,[24] initially partnering Stefano Coletti and later Roberto Merhi, Robert Vișoiu and Álex Palou.

[26] Boschung picked his highest finish of the season with seventh in the feature race at the Red Bull Ring.

He was set to claim another points finish, running in ninth during the feature race, but he was forced off track by Jordan King and lost five places.

[29][30] Boschung parted ways with Campos before the final round at Yas Marina and was replaced by that year's FIA Formula 3 European champion Lando Norris.

[33] After appearing at the 2017 post-season test with MP Motorsport, Boschung signed with the team for the 2018 season alongside Roberto Merhi and later Dorian Boccolacci.

He dropped to ninth due to excessive tyre wear, but was upgraded to eighth after Sérgio Sette Câmara was disqualified.

From Spain to France, Boschung suffered five consecutive retirements ranging from racing incidents to car issues.

[44] At the second round in Baku, despite qualifying in the top 10 once more, he was hit by his teammate Alesi and fell to the back on the opening lap of the feature race.

[45] Boschung maintained his top 10 qualifying form at Barcelona in eighth before being promoted to seventh for the feature race.

[48] Boschung had a weekend to forget in France, being eliminated in the start chaos in the feature race and finishing 15th in the sprint.

[49] Once again, his season was again plagued by funding problems, and he was replaced with Ryan Tveter and Dorian Boccolacci for the rounds in Austria and Britain respectively.

[50][51] Boschung returned to Trident at the Hungaroring round, where he retired with an engine failure in the feature race and finished 18th in the sprint.

[52][53] At the Spa-Francorchamps feature race, Boschung was involved in an accident which resulted in the death of Anthoine Hubert and serious injuries for Juan Manuel Correa.

Boschung was running well in the opening laps but sustained front wing damage in an incident with Ticktum and was forced to pit.

But at the halfway mark of the race, Vips passed him back and Boschung started to tumble down the order, citing brake issues, and eventually finished 15th.

[74] Boschung finished the feature race in ninth place after managing to defend his position during the final few laps.

[77] In November 2021 Campos announced that Boschung would be remaining with the team for the 2022 campaign, partnering new Alpine junior Olli Caldwell.

Boschung finished eighth in the sprint race but was given a 20-second time penalty after being out of position during the starting grid, demoting all the way to 15th.

[82] In the feature race, a set-up change saw Boschung unable to maximise his opportunity and lacked pace to finished 14th.

He was able to turn his fortunes in the feature race, making another lightning getaway to move into second on the opening lap behind Roy Nissany.

[87] Just a week later, Boschung raced in Monaco, qualifying tenth following penalties and was set to start on reverse pole.

[94][95][96] Boschung took advantage of reverse grid pole to achieve his second podium of the season with third place in Saturday's sprint race.

[98] In Zandvoort Boschung had an uneventful weekend, a poor qualifying result only bringing him 17th and 15th places in the sprint and feature races respectively.

[99] Boschung had an unfortunate showing in Monza, he retired in the sprint race was involved in an incident with Clément Novalak which bent his steering after starting 13th.

[100] In the feature race, Boschung was forced off-track and re-joined in an unsafe manner, and later crashed into the barriers after colliding with Pourchaire.

[108] Talking about his weekend, Boschung described his car as "incredible", saying that the team's baseline race pace was better than it had been during the previous season.

[109] In Jeddah, Boschung qualified in ninth, and took the standings lead after finishing in a strong fourth place during the sprint race.