Am I able to get the Mass Effect Insanity Difficulty Achievement this way on the Xbox 360?

I wanted to do a playthrough of mass effect on insanity difficulty, but i wanted to go through hardcore mode first to get the hardcore achievement. Would I be able to finish the hardcore achievement, then start a new playthrough with the same character and put it on insanity, because it says not to change the difficulty, but it doesnt give you an option to put your difficulty what you want it to when you start a new playthrough with your other character, will i still get the achievement if i start a new playthrough? On the Xbox 360.
You can