Meagher was expected to compete for medals at the 1980 Olympic Games in Moscow, Russia. However, Meagher, along with the rest of the United States Olympic team, never got her chance due to American-led boycott of the Olympics. However, in 1981 Meagher gave one of the most memorable performances in competitive swimming at the U.S. Swimming National Championships held in Brown Deer, Wisconsin in 1981. At the meet, Meagher set world records in both the 200 meter and 100 meter butterfly, the two primary distances at which the butterfly is contested in competitive swimming. The times for both records were considered astonishing, especially the record of 57.93 seconds that Meagher set in the 100 m. Both times would stand for nearly two decades - American swimmer Jenny Thompson broke the record in the 100 m in 1999 while Susie O'Neill of Australia set the record in the 200 m a year later. Some have argued that Meagher's records in the butterfly were among the most impressive records ever set in sport, let alone swimming, ranking among such noteworthy records as Bob Beamon's long jump world record in 1968. This led to her being named Female World Swimmer of the Year by Swimming World magazine, which she again won in 1985. She swam collegiately for UC Berkeley, graduating in 1987 with a BA in Social Sciences.
At the 1984 Summer Olympics in Los Angeles, California Meagher won gold medals in both the 100 m and 200 m butterfly races, along with another gold by swimming the butterfly leg of the women's medley relay. Returning to compete at the 1988 Summer Olympics in Seoul, South Korea, Meagher won a bronze medal in the 200 m butterfly. By the time she left competitive swimming, Meagher had won 24 US national swimming titles.
Meagher married former speed skater Mike Plant; they now live in Peachtree City, Georgia with their two children Maddie and Drew. Meagher is also the sister of former Kentucky Republican Representative Anne Northup. There is a swimming complex in Louisville named for Meagher, as well as a street in Elizabethtown, Kentucky.