Junko Tabei was the first woman to climb to the top summit of Mount Everest (Sagarmatha) in Nepal/Tibet. Junko was born in 1939 in Fukushima Japan and began climbing in her 30s. She has climbed many mountains to date. Some of the tallest are Mt. Fuji (Japan), Erta Ale (Ethiopia), Puncak Jaya (Indonesia), and the Matterhorn (Switzerland). Junko started a women's climbing club in the late 60's called "Ladies Climbing Club" and went with an expedition of women in 1975 to climb mount Everest (Sagarmatha). They spent months training and preparing for the expedition. Two special things about this woman's achievement.
One, it is hard as hell to climb/ hike to high elevations. You carry gear with you for eating, sleeping, etc and you must take your time using safe routes to reach the top. The mountains she climbed were the most enormous in the world, with Everest measuring in at over 29,000 feet high. There are hundreds of people who even with the help of local Sherpa's (guides) die trying to make this trek. It is incredibly difficult.
Two, at the time when Junko climbed the mountain she was battling a lot of sexism in Japan (and the world). In her country women were viewed as less than. Men did not view women with the respect they do now. They thought women should be at home, blah blah, blah. Junko made this climb anyway, with her 3 year old daughter at home with her husband who was also a mountaineer. Juko is still climbing and leads an organization called the "Himalayan Adventure Trust of Japan" which helps support the trips of students who wish to climb, and the Sherpa's who help people survive the treacherous climb.
Sources: NBC News (site), Wikipedia (Site), Japan Times (Site)