Shushunova was unable to compete at the 1984 Summer Olympics, which were boycotted by the Soviet Union. Instead, she competed at the "Friendship Games", where she finished third in the all-around event.
The following year, she made her breakthrough, winning 4 titles at the European Championships and three at the World Championships, including the all-around title, which she shared with compatriot Oksana Omelyanchik.
She lost her world title in 1987, finishing second to Aurelia Dobre of Romania, but was still a top contender for the all-around title at the 1988 Summer Olympics in Seoul. There, a close battle for the title developed between Shushunova and Daniela Silivaş (Romania). After Silivaş received a score in her final event by many considered to be too low, Shushunova won the title by 0.025 points. The Soviet team won the team event, and Shushunova earned two more medals finishing second in the balance beam and third in the uneven bars.
Shushunova retired after the Olympics and currently lives in St. Petersburg.