These achievements unfortunately DO NOT stack. However, once you play through the game once (go with Casual to make it easy on yourself), you can use level select to choose the final part of each individual level on the other difficulties to get credit for them. Once you have done this with all six missions, you get the next difficulty achievement. The levels do not have to be done in order or at the same time. You can do two in Red, then switch to Orange and so on, just so long as they all get done at some point.

~Int