He may have been born in Milan, but first surfaces in Vienna, in a letter exchange between the famous violinist Johann Heinrich Schmelzer of the Viennese court and Karl II von Liechtenstein-Kastelkorn, Prince-Bishop of Olomouc.
That he was introduced to the Prince-Bishop, a well-known collector of music, and knew Schmelzer, one of the most important musicians at the court, seems to indicate that Albertini was much respected in Vienna.
Nothing is known about his career, except that at some point he entered the service of Eleanor Gonzaga, widow of Ferdinand III, as chamber musician, and held that position until his death, which occurred in Vienna on 22 September 1685 when Albertini was murdered.
As a composer Albertini is known by a single collection of music, the twelve Sonatinae (sonatas for violin and basso continuo) posthumously published in Vienna and in Frankfurt in 1692.
The collection was prepared for publication by Albertini himself, but he did not live to see it printed, possibly because of the high cost of the copperplate engraving process.