Achatz was the first flutist in the Stockholm Concert Association 1920–1941 and 1954–1962 and in the Vienna and Berlin Philharmonic Orchestra 1941–1944 and in the Royal Court Chapel 1944–1954. He became a Swedish citizen in 1927. Achatz was elected as Associate No. 213 by the Royal Academy of Music on May 19, 1960, was awarded Litteris et Artibus in 1964 and became a regular member No. 762 of the Academy on July 1, 1971. Achatz was a professor in Vienna and Porto and worked both as an educator and conductor.

Carl Achatz was the father of pianist Dag Achatz and choreographer Susanne Valentin. From 1955 he was married to the artist Eléna Michéew.