Each case has a few workable conclusions, but only one correct one. You can choose a conclusion, see how it plays out, then make another choice, without affecting your progress. On the screen at the end of each case, you have the option to hold the Back button to check if your conclusion was correct (it will turn green) or to press X to choose another ending or A to finish the case.
(The achievement text is weirdly phrased; it might be clearer to say "the one
correct conclusion for each
The six correct conclusions are:
The achievement doesn't pop until after the credits after the last case, so don't panic when it doesn't pop right after the last cutscene.