First off I'm going to state I absolutely suck at FPS games. That said:
so far that I'm aware, there doesn't seem to be a reason to play any difficulty level other than Hard if you're achievement hunting in the single player campaign. There doesn't seem to be any permanent death, so if you drop a mob and come back, drop another, come back and so forth over and over, it seems you'll at least eventually get the completion of the acts.
The "Public Housing Authority" achievement is obtainable at the second mission, when you're securing the crash site. When you see that you have points/money/whatever it is called in the bottom right corner, just deploy 2 of the turrets close together (I just panned away from the first deployed until the red turned green and dropped). Once the second turret opens up, achievement should unlock. For those not looking at the manual, push up on the directional pad to open the purchasing menu