To collect this achievement, you need to finish Story Mode. Story Mode is the only option available to you at the start of the game until you finish Story Mode and unlock Payload and Classic Mode.
To finish quickly, prioritize a lighter body (glider worked well for me) until you get enough money to afford 4 of the best boosters and stages, along with the nuclear powerplant. Upgrade them as much as you can, and then switch to the spaceship to tank through obstacles.
Once you have all this stuff, launch and let your stages carry you most of the way before activating your boosters. Your boosters do the most the lighter you are.
Then watch the closing cinematic, collect your achievement, and move on to the others!
(There are probably more optimized ways to do this, but this is the one that worked for me. Comment with any changes you want me to make!)