Andreas Däscher took up ski jumping in 1943, but had to wait until the end of World War II to compete internationally. He took part in the first of his four consecutive Olympic large hill tournaments at the 1948 St. Moritz Games, where he placed 17th. He would later place joint-16th (with Janez Polda of Yugoslavia), 6th, and 20th in 1952, 1956, and 1960 respectively, and was the flagbearer for Switzerland in the opening ceremony of his final edition. His most significant accomplishment, however, came on March 3, 1950, when he set the world record for distance at 130 metres/426.5 feet. Domestically, he was a nine-time Swiss national champion.
Däscher is probably even better known for developing the Däscher technique, or the parallel style jumping technique that was used commonly through the early 1990s, when it was replaced by the V-style. By career, he was a plumbing and heating fitter. His brother, Hans, was also a ski jumper who represented Switzerland at the 1952 Oslo Games.