I have had zero trouble in old school except for chapter 13, namely this guy. I can kill the cops in the room no problem but i get butchered with no last man standing, which is how i beat him on hard. I even replayed the level and SAVED a RPG, went into bullet time, hit him and he survived that!
I did this on hard, not sure how it will work for old school. I took out the standard cops with a pistol, using very little bullet time. When he entered I used the shotgun and peppered his face as many times as I could. Then I dove backwards with the pistol before bt ran out and shot at his face and he died.
Not sure if it's the neck or you having to hit the face shield a certain amount of times.
When I played through on hard I hung on to a grenade launcher for the later inside portion of the police station, it made short of work of the heavy. Even if the heavy can survive an RPG, I'm sure he wouldn't do well against a barrage of grenade explosions on Old School.