This achievement entails you to find 25 secret areas hidden within the campaign. You will know when you find one of these because the words "Secret Area" will appear across your screen. You can check your progress towards this achievement within the statistics.
Also, some levels like "Oriental castle" and "Colosseum" require you to find all secret areas for the tarot card. So it's really worth getting those tarot achievements done while going for this.
The videos I am about to post are not mine, but I thought I would pass them a long for anyone who wants to get this achievement out the way ASAP. I used them and found them to be a great help. You can thank "Painkillerzone" for the videos.
Also, just to clarify, the levels "Opera House", "Colosseum", "Oriental castle" and the bonus level "City on the water" all require you to find the secret areas for one reason or another.