Considering the way that Alan Wake plays out there is absolutely no reason for you to ever play on the Hard difficulty. Difficulty achievements stack, meaning you only need to beat the game twice - once on Normal or Hard unlocks Nightmare and then play through Nightmare.
Playing through the game on the Normal difficulty will allow you to get most of the other achievements in at least one run, including the manuscript and other collectible achievements. Go back, play any Episode you need to get achievements you've missed and then move on to Nightmare. Skip over Hard entirely since it's somewhat redundant.
The only difference difficulty level makes is how hard it is to defeat the Taken. On Hard enemies have about 50% more health and on Nightmare they have around twice the health they do on Normal. There are also 15 new manuscript pages to collect on Nightmare but that's for another guide.