I got the achievement by doing just the 'fast replay' levels on my third playthrough (having already beaten easy-solo) of the game. I did them in a different orders, some in co-op and some in single player. It unlocked after beating level 8. You definitely do not have to play it start to finish. Getting a lower grade in a chapter doesn't wipe out the higher score you already obtained.
Best thing I can tell you is to write the grade down for each chapter and mark it off as you get an A - it's probably just one level that you're missing.