She had already been to the top of the world. Alison Hargreaves, a 33-year-old Scot, last May became the first woman to climb Mount Everest alone and without oxygen tanks. But she had her sights set on the two other Asian peaks-Mount Godwin-Austen (K2) in Pakistan this summer, and then Mount Kanchenjunga in India later this year-that would earn her a rare mountaineering trifecta. Because of its unrelenting steepness and treacherously sudden storms, K2, known as the "Killer Mountain," is a formidable challenge for even accomplished climbers. Of the thousands who have tried to scale it, only 113 have reached its 8,611-m-high summit, and 38 have died on its slopes. Last week Har greaves added to those grim statistics. Some 600m into her descent from the peak, she was overcome by an avalanche that is believed to have also killed six other climbers.

Three separate expeditions-from the U.S., New Zealand and Spain-were near the summit of K2 on Aug. 13, when heavy winds started to pound against the mountainside. Peter Hillary, son of Sir Edmund Hillary and leader of the New Zealand group, began his descent as soon as the weather shifted, and he reached the base camp safely. Separated from Hillary, two New Zealand climbers met up with Hargreaves and Rob Slater, an American who had invited her to join the assault on K2. Shortly thereafter, the four, along with all three Spanish climbers, were swept to their death.

None of the organizers waiting in Skardu-the nearest town, 100 km from K2-knew what had happened until Hillary called from the base camp. He said that there were reports that climbers had seen Hargreaves' body hanging from a remote ledge near the 8,000-m mark. "Peter said the weather and the wind on the mountain were appalling," says Sir Edmund, who was the first person to conquer Everest, in 1953, but who never attempted K2. "These things can happen on any big mountain ... Just because [Hargreaves] was a success on Everest doesn't mean she was going to strike it lucky on K2."

Hargreaves, who began climbing professionally at 18, believed she could manage the risks. "If I thought it was desperately dangerous, I wouldn't do it," she told a reporter before leaving for K2 last June. The mother of two, she brushed off critics who claimed she was selfish for indulging in such a perilous activity. When she reached the summit of Mount Everest, the first radio message she sent was to her two children: "I am on top of the world, and I love you dearly."

Hargreaves' husband Jim Ballard quotes a favorite saying of hers: "It is better to have lived one day as a tiger than a thousand as a sheep." She clearly lived by that rule to the end. "She was actually where she wanted to be," says Ballard. "She was on her way down. At least inside she would have had the happiness of reaching the summit." Because a recovery attempt would be too dangerous, the bodies of Hargreaves and the others will forever remain on the mountain they climbed but could not completely conquer.

-By Julie K.L. Dam. Reported by Meenakshi Ganguly/New Delhi, Helen Gibson/ London and Simon Robinson/Auckland