These achievements are only related to completing the stages of Odyssey mode. When you enter into Odyssey mode, you are given three lives, losing one each time you crash the planes. Three crashes and your game is over. Fortunately, the game does allow you to start Odyssey mode from the beginning of the highest stage you made it to. So you just need to finish each stage without using all three of your lives to progress. When you are in the game mode selection screen, a bar will appear above which you can choose the stage you want to start on.
Know that completing a stage has nothing to do with score or landing a certain amount of planes; it is only based on time. For this reason, there is a way to make completing the levels much easier. See "Master Pilot" for more information.