Eberle, a pupil of the famous husband-wife coaching team Béla Károlyi and Márta Károlyi before they defected from Romania to the United States, was the first female Romanian gymnastics star to succeed Nadia Comaneci, although she was often in Comaneci's shadow as for the greater part of Eberle's career, they competed together. Despite this, she made a name for herself, garnering 13 individual medals at the European/World/Olympic level. Most notable among her accomplishments was her winning the Floor Exercise title at the 1979 Worlds ahead of her legendary contemporaries Nelli Kim and Maxi Gnauck as well as earning a silver medal on uneven bars at the 1980 Olympics, being narrowly edged out of gold medal place by Gnauck.
She was also on the gold medal winning team at the 1979 World Championships held in Fort Worth, Texas, USA. Despite her fall on the balance beam in the team optionals segment of the competition, other scores of hers were strong enough to keep the Romanian team in contention for the gold with the Soviet team. Ultimately, her compatriot Comaneci came back from an injury, having competed only in the compulsories segment of the team competition and having abstained from competing on any of the other apparatuses during the optionals segment of the competition, and competed on beam getting a very high score of 9.95, allowing the Romanians to scratch Eberle's lower score and win the gold medal. In any event, Eberle did help her team to a rare victory over the Soviet team, which was one of the Soviet team's only three world or Olympic title losses from 1952, when a full women's gymnastics program was first held at the Olympic games, to 1992, which was the last appearance of the unified Soviet team (under the guise of the Commonwealth of Independent States).
Although a strong gymnast all-around (being silver medalist in the all-around twice in 1979 - at that year's World Cup and European Championships), she was especially noted for her work on the uneven bars where her routine could vary greatly from year-to-year with a very different set of skills from competition to competition, including her often very quick and unusual transitions from one bar to the other.
Like the Karolyis, Comaneci, and others, Eberle defected from Romania, in 1989, to Hungary, and then to the USA two years later, in 1991. She is married and had a son, Roland, in 1999, and coaches in California with her fellow expatriate Romanian, gymnastics coach and choreographer Géza Poszar.