He learned the game of chess as a child in Königsberg, and by the time he went to Berlin in 1859 to study, he was already a very strong player and theoretician.
He was in the editorial department of the Deutschen Schachzeitung, where he published analysis of opening theory.
During his time in Berlin, he played matches with Carl Mayet and Berthold Suhle (+0 -7 = 2) in 1860, and with Adolf Anderssen (+10, -14, =5) and Gustav Neumann in 1861.
Hirschfeld also played individual games against Wilhelm Steinitz, Johann Jacob Löwenthal, Bernhard Horwitz and Cecil De Vere.
In 1873 he took up permanent residence in London, where he was a frequent analysis partner of Johannes Zukertort.