Her grandfather was the chief choreographer of the Kazakh National Conservatory, and her paternal great-grandfather was a deputy of the Russian State Duma of the first convocation.

After graduating from college, Galina Sidorova married a military man, during World War II on the Eastern Front.

There Galina began to dance in the ballet troupe of the Abay Opera House and, having divorced her first husband, married Abduakhim Asylmuratov.

Asylmuratova became more popular in Western theaters than in those of her home country due to her frequent guest appearances abroad, including Roland Petit's company.

Her repertoire included all the classical ballet rôles in Swan Lake, The Sleeping Beauty, Giselle, Don Quixote, and La Bayadère, Mikhail Fokine pieces such as The Firebird and Les Sylphides, as well as modern classics like Romeo and Juliet, works by choreographer George Balanchine and Roland Petit.

Among Asylmuratova's partners were dancers Konstantin Zaklinsky, Farukh Ruzimatov, Evgenii Neff, Igor Zelensky, Makhar Vaziev (in St. Petersburg), Irek Mukhamedov (in London), and Jan Brex (in Marseille).

In the same year, at the peak of her career, Asylmuratova left the stage and took up teaching at her alma mater, the Vaganova Academy of Russian Ballet.