Tatarskiy was born in Kiev into a family of Jewish origin. His father Mikhail Semyonovich Tatarskiy worked in circus and wrote gags for such clowns as Oleg Popov and Yuri Nikulin who was a close family friend. In 1974 Aleksander graduated from the Kiev Institute of Theatre and Cinema and in 1975 he finished 3-year animation courses at Goskino. From 1968 to 1980 he worked at Kievnauchfilm under the director David Cherkassky as an artist and animator. Among his works of that time was Adventures of Captain Wrongel. During the studies he met Igor Kovalyov who became his close friend and a co-author on many projects. Together they recovered a camera from the studio's junkyard, built a handmade animation stand and created their first "underground" animated film Speaking of Birds in 1974. It wasn't released to public; instead they showed it to several prominent animation directors from Soyuzmultfilm who booked them two places at High Courses for Scriptwriters and Film Directors. Nevertheless, Kievnauchfilm refused to let Tatarskiy go. In 1980 Kovalyov went to Moscow alone. Shortly after Tatarskiy arrived on his own. He managed to get work at Multtelefilm division of Studio Ekran with the help of Eduard Uspensky who wrote the screenplay for Tatarskiy's first director's effort — Plasticine Crow, which also happened to be Soviet first claymation film. After the enormous success Tatarskiy was offered to create new opening and closing sequences for the popular children's TV show Good Night, Little Ones! also made of plasticine; they were later included into the Guinness Book of Records by the number of broadcasts. It was followed by two other claymation shorts: New Year's Eve Song by Ded Moroz and Last Year's Snow Was Falling. From 1984 on he worked in traditional animation only. In 1988 Tatarskiy, Kovalyov, Anatoly Prokhorov and Igor Gelashvili founded the Moscow animation studio Pilot, the first private, independent film studio in the Soviet Union aimed at adult-themed comedy movies. Tatarskiy took the role of artistic director which he kept till his death. Most films created at the studio received festival awards. Shortly after the team was offered to work at the Klasky Csupo studio. And while Tatarskiy refused to leave Pilot, Kovalyov and many other animators left for the United States. In his interviews Tatarskiy called it a great tragedy for the Russian animation industry which was already in poor state by that time. During the 1990s Pilot produced mostly advertising and music clips. In 1997 Tatarskiy launched a side project — Pilot TV that specialized in 3D animated television shows. Its first program, Fruttis Attic, ran from 1997 to 1999 and featured Pilot Brothers, two "virtual hosts" based on the characters from Investigation Held by Kolobki who interviewed real-life celebrities. Tatarskiy served as an artistic director and in 2000 launched another similar project — Turn off the Light!, a political satire loosely based on Good Night, Little Ones!. It ran for three years and won two TEFI awards as the best entertainment program in 2001 and 2002. The Red Arrow spinoff ran for a year and also won a TEFI in 2004. In 1997 he was also given Nika Award for his animated shortPilot Brothers Make Macaronies for Breakfast which was part of the Pilot Brothers mini-series. Tatarskiy was also the founder of :ru:Гора самоцветов|Mountain of Gems, Pilot's biggest project made with the support of the State Committee for Cinematography. From 2004 till this day over seventy 13-minute animated shorts were produced based on fairy tales of Russian people and other ethnic groups that populate the Russian Federation and former Soviet states. Every short features its own art direction and animation technique, from stop motion and traditional animation to computer and cutout animation. They are united by claymation openings that tell the history of every specific region. Among the animation directors who took part in the project were Eduard Nazarov, Konstantin Bronzit and Tatarskiy himself. Tatarskiy died of a heart attack aged 56. He was buried at the Miusskoe cemetery in Moscow.