Brambilla was born in Cassano d'Adda, the daughter of Gerolamo and Angela Brambilla. She was the fourth of five sisters, all of whom became opera singers. Marietta was a contralto who specialised in travesti roles. Teresa was a soprano who created the role of Gilda in Rigoletto. Both had very prominent careers. Annetta and Lauretta were both sopranos who had lesser careers, appearing primarily in provincial Italian opera houses. The family moved to Milan in 1828, and Giuseppina had hoped to train at the Milan Conservatory where both Marietta and Teresa had gone. However, she was not accepted when she auditioned in 1833 and consequently studied singing privately. Her first public appearance was in Vienna on 13 May1839 when she sang with her sister Marietta in a concert celebrating the name day of Prince Metternich. She made her operatic debut in August 1840 at the Teatro Ricciardi in Bergamo, singing the soprano role of Sinaide in Rossini's Mosè in Egitto, a role she repeated in October of that year at the Teatro Grande in Trieste. The following month she appeared there in the contralto role of Maffio Orsini in Donizetti's Lucrezia Borgia, a role which had been created by her sister Marietta in 1833. She appeared in Rome's Teatro Apollo, again as Sinaide, in January 1841, and in April made her La Scala debut as Lisa in La sonnambula. Later in the season there she created the role of Elisa in Giuseppe Manusardi's Il biricchino di Parigi. She then left for Spain where she was the leading prima donna in multiple productions in Barcelona from November 1841 until January 1845. She then sang for a season in Valencia before returning to Italy by way of Paris and London. She made her London debut in July 1846 at Her Majesty's Theatre reprising the role of Maffio Orsini in Lucrezia Borgia. Her Paris debut followed in October of that year when she appeared at the Théâtre-Italien as Abigaille in Nabucco. On her return to Italy she sang in several provincial theatres before accepting a contract as the prima donna with the Italianopera company at the City Theatre in Odessa, where she was particularly popular and appeared in multiple leading soprano roles from 1850 through 1851. The 1852–1853 season found her in Jassy, where again she proved very popular. She returned to Jassy in the 1855 season to appear in four more operas, including Il trovatore where she sang the role of Leonora with the Italian tenor Corrado Miraglia as Manrico. She married Miraglia in 1857 and retired from the stage five years later. Her last performances were at the Teatro Carlo Felice in Genoa where she sang Isabelle in Robert le diable, Delizia in Ricci's Corrado d'Altamura, and Amina in La sonnambula. Miraglia died in 1881. Brambilla lived on for another 20 years. Her death in Milan at the age of 84 was announced on 11 April1903.