Start the first level, drop down the chute, kill all enemies in the street, then jump up to the ledge outside the first secret area (above the big brown box to the right of when you drop down to the street)

Now, save on that ledge, then enter the secret room/area. It will count +1 to the achievement. Load the save, and enter again. Once again it will count it +1 towards the achievement. Rinse and repeat until you get the achievement.

This works for every secret area; however you MUST remember to save right before you enter the secret area(s) to be able to do this correctly.