Warning: Do not bother grinding this out without just playing the game!
There is no efficient way to grind this achievement out early. There isn't a specific challenge available before you'll unlock this naturally. If you're intending to beat or complete the game, let this come naturally. If you're looking for easy achievements, this isn't one of them.
For reference, I finished the requirements for 1 star on six hospitals, then went back and tried to 3-star the early ones with my new experience before. After a few attempts on them, and a cumulative 20 in-game years played on them, this achievement unlocked. See why this shouldn't be attempted if you aren't playing the game normally?
Now, some information: Reception, General Practice, and General Diagnosis do not count towards this. All of the miscellaneous rooms that don't cure patients won't help either. However, all of the other rooms count. So whether you're grinding out early or late game hospitals, you'll put a good dent in this achievement. Restarting levels also count towards this achievement, for those of you going for perfect builds.