This achievement must be done on Easy or Medium (I would recommend doing it on Easy). All of the heart containers are in big chests that you have to pogo jump on to open. Also, on all of the levels except for the Moon level, the chests containing the heart containers are behind what appear to be walls, but if you walk into the "wall" will reveal themselves to be secret passages.
Here is a YouTube link showing where to get this achievement. Video by windtalgia, it shows the locations well.