These achievements are awarded for 100% completing each world of the game. Getting 100% on a level is done by collecting all of the blobules on the level and then making it through the green pipe at the end. To 100% a world, you must 100% the first 10 levels. Once you finish the first 10 of each world, 3 additional, more unique levels are unlocked, but are no required to be played for the achievements.
The blobules are almost always easy to find. They are not well hidden at all. If need be, use the binoculars button in the top right corner of the screen to zoom-out and see what is around you. Remember, you must make it through the green exit pipe after collecting all the blobules on the level for it to count.
You can check your completion percentages on each level of the game from the Arcade Mode level selection screen.