She competed in the shot put at the 1952, 1956, 1960 and 1964 Olympics and finished in first, second, seventh and third place, respectively. In 1952 she also finished fourth in the javelin throw.
Between 1952 and 1956 she set eight consecutive world records and 14 national records in the shot put. In 1953, she became the first woman to throw over 16 meters (1620 m). During her entire career as a competitor and coach Zybina accentuated on technique rather than strength.
She was left out of the Soviet team before the 1968 Olympics and retired 1969, because of her age, although she was still a second Soviet shot putter. In retirement she worked as athletics coach in Värska, Estonia. Zybina was married to Yury Fyodorov, a Russian captain and commander of the Russian cruiser Aurora in 1964–85.
The cruiser was famous for starting the 1917 October Revolution, but by 1960s was a museum ship. In 1959 she gave birth to a son, which partly explains her poor performance at the 1960 Olympics.