Myshkin came to prominence in the late 1970s when he earned a spot on the Soviet national team as a backup to the legendary Vladislav Tretiak. On February 11, 1979, he was the surprise choice of coach Viktor Tikhonov to start in the deciding game in the Challenge Cup tournament against the National Hockey League all stars. Myshkin responded with a sterling effort, shutting out the NHL stars 6-0 to win the Challenge Cup for the Soviets. A couple of months later, he won his first of six World and European championships, the others coming in 1981, 1982, 1983, 1986, and 1990.