Start a play through of this game, it's about 45 mins long
You will go through the game in a random order, not playing each level
When the game ends you'll get the achievement for beating the game and an achievement for every level that you played. You will also unlock stage selection after beating the game. You can select the stages you didn't play (the ones with question marks on them) and start them and quit out to get the achievement for seeing each level
You can pause on a level to get the level specific achievement, as seen in the video at 1:40, or you can wait until you complete the game and they'll all pop at once
Achievement Walkthrough: