The most important achievements in the space race are to walk on the moon, living in space, and the first American to explore space. These achievements in clued Apollo 11 International space station and the freedom 7. These are the most important achievements because they were part of history. The most important achievement was the Apollo 11. It was important because they had tested 9 missions and they had all failed but then Apollo 11 was a success. According to an article, it says that this was NASA biggest achievements because "Apollo 1 was launched in 1967 but ended in a disaster when all 3 astronauts died in a fire on the launch pad." (listovative.com). Apollo 1 was not a success because it had killed 3 astronauts and the 11 did not