i looked into this- sorry about the complication. These are the kind of issues I learn from as I make games.
You do have to complete each hole before the music ends for each hole (2,5, and 7) while the game is running. If you turn off the game while trying to get it, you'll lose progress. But you can go back and forward in menus. To do each hole, you have to finish grabbing the ball out of the hole before the music ends. But you can quit to the menu immediately after. Once you see the achievement in the achievement window, you need to go to visit level (or just hit begin to go to the first level) to save the achievement for real.