Akhedzhakova was born in Dnipropetrovsk, Ukrainian SSR. She grew up in a theatrical family in Maykop, Russian SFSR. Her stepfather, Medzhid Salehovich Akhedzhakov (1914–2012), was a Circassian nobleman who served as the Principal Director of the National Theatre of the Republic of Adygea. Her mother, Yuliya Alexandrovna Akhedzhakova (1916–1990), was also an actress at the same drama theatre. At the age of 10, when her mother and aunt was suffering from tuberculosis, she wrote a letter to Joseph Stalin with a request for help. In response, a rare drug was delivered to her family.
In 1956, she entered the Moscow Institute of Nonferrous Metals and Gold where she studied for eighteen months. She first appeared on stage in 1961 at Moscow Youth Theatre. In 1962, she graduated from Lunacharsky State Institute for Theatre Arts (GITIS). Her first film appearance was in Ishchu cheloveka (1973) (Russian: Looking for a Man). Her debut in this drama was awarded several prizes at international film festivals in Locarno, Switzerland and Varna, Bulgaria. In 1977, she joined the Sovremennik Theatre. In 1986, she played four main roles in the play Apartment Columbine, directed by Roman Viktyuk.
As a film actress, Liya Akhedzhakova became widely known due to her roles in Eldar Ryazanov's films, including Tania in The Irony of Fate (1975), Verochka in Office Romance (1977) and Fima in Promised Heaven (1991). In the 2000 film Old Hags, she played alongside her stepfather.
Her relatives include Murat Kazbekovich Akedzhak, Deputy Head of the Administration of Krasnodar Region, and George Akhedzhak, Honored Coach of the USSR.
Akhedzhakova's first husband was Valery Nosik, an actor of Moscow Pushkin Drama Theatre and Maly Theatre. Her second husband was artist and poet Boris Kocheishvili. In the summer of 2001, Liya Akhedzhakova married the Moscow-based photographer Vladimir Persiyanov. She has no children.
Akhedzhakova became politically active when Boris Yeltsin came to power. During the 1993 Russian constitutional crisis she attended a live TV show where she gave a speech in support of Yeltsin's actions, encouraging the army to «protect us from the goddamn Constitution» and start storming the White House, or «the Communists will return». As a result of the armed conflict, from 158 to 2000 people (mostly civilians) were killed and hundreds were injured. It also led to a forceful liquidation of the Soviet model in Russia. The actress has been personally blamed by her opponents for escalating the conflict ever since.
Akhedzhakova is a critic of the contemporary Russian politics and Vladimir Putin in particular. Together with Eldar Ryazanov, Yuri Shevchuk, Andrey Makarevich, Andrey Konchalovsky and others, she protested against Russian policy towards Ukraine. Following the shootdown of Malaysia Airlines Flight 17, she publicly read a poem of Andrey Orlov, Requiem for MH17 that ends with words «I'm guilty, because I'm Russian». In 2013, Akhedzhakova received a prize from the Moscow Helsinki Group for "the protection of human rights by means of culture and arts".
Eldar Ryazanov characterized Akhedzhakova as follows: "She sympathizes with the weak, and despises the cruel. In that her artistic credo coincides with the stance of the great Chaplin".