#3 Monica Seles
No other tennis player barring Monica Seles has won 8 or more Grand Slam titles before turning 20. Very few people start playing at the highest level and challenge the top players immediately after turning professional. But that is exactly what Monica Seles accomplished.
In 1990, she became the youngest ever French Open women's singles champion by winning the title at the tender age of 16. She retained her title at Roland Garros the following year.
Seles came to the US Open in 1991 as the second seed behind her great rival Steffi Graf. She beat Americans Jennifer Capriati and Martina Navratilova in the semi-final and final respectively to win her first US Open title at the age of 17 years, 9 months, 5 days.
#2 Martina Hingis
There are quite a few women who became World Number 1, won multiple Grand Slam titles in their teenage unlike in the men's field where they are few and far between. One such tennis prodigy was the first tennis superstar from Switzerland -- Martina Hingis.
Hingis won the Wimbledon doubles championships in 1996 when she was not even 16 years of age. The following year proved to be her best ever as she made the finals of all 4 Grand Slams, winning all but one.
Hingis entered the 1997 US Open as the top seed. Hingis won the competition without dropping a single set, beating Venus Williams in the final. Hingis was only 16 years, 11 months, 8 days old at the time of her first and only US Open triumph.