He first studied piano with Nikolay Dubasov; Anna Essipoff; Anatol Liadov in composition; and Maximilian Steinberg in orchestration.

[1] After three years of service in the Russian army, Achron graduated from the conservatory in 1918 and went on a concert tour of Russia and Germany.

[1] On New Year's Eve 1923, he played in Carnegie Hall as an accompaniment for Jascha Heifetz annual solo violin performance.

[2] For the next ten years, he served as Heifetz's principal accompanist, recording an extensive discography and performing chamber and solo recitals in major music centers all over the world.

His program encompassed three Bach transcriptions: that of the chaconne by Busoni, the prelude and fugue in A minor by Liszt and the overture from Cantata No.

[4] He performed his original works with the New York Philharmonic at Town Hall in December 1937, with Sir John Barbirolli (1899-1979) conducting.

On January 20, 1940, he and his wife performed at Carnegie Hall for the fourth annual music festival for the Trade Union Division of Jewish Workers and Pioneers in Palestine.

[9] Amidst all these performances, Achron remained active as a composer, writing the song "Do You Know that The Moon Can Talk" under a pseudonym, John Dorr.

It was published in 1937 by Chappell & Co., Ltd.[1] In 1941 he composed two compositions for violin: Sonet #2, introduced by Jascha Heifetz and "Valse Dramatique" performed by Mischa Elman.