Deadly Premonition

You can have the Infinite Wrench and the Radio before the hospital. Together, they make the rest of the game trivial. The Infinite Wrench will kill early zombies in about 2 hits on hard, or about 4 hits for late-game zombies. I actually got worried around the time of Harry's Mansion on my hard play-through, thinking that I had somehow changed the difficulty by mistake.

The only weapons you need for normal enemies are Infinite Wrench for normal zombies (obtainable by completing the quest chain that starts with finding Anna's dress and diary at her home around noon) and Wesley Special for wall crawlers (obtainable by collecting all 7 bones and turning them in to Brian at the graveyard at any time after the Lumber Mill).

For boss fights I recommend also having the Infinite Magnum, obtainable by collecting all 7 bones and then allowing Willie to steal them at any point after the Lumber Mill. When you retrieve them from Kaysen's truck, you will find the Infinite Magnum. You can probably get by with Emily's gun instead, which you will automatically obtain before the game's important boss fights.

The weather doll is nice to have and makes first aid kits almost unnecessary, but is unobtainable until after the Lumber Mill. Grecotch (Keith's guitar) does high damage but its attack speed is so slow that it is not very useful against infinite spawns.

Don't forget that you can hold your breath to confuse zombies. This is pointless on easy or medium difficulties, but indispensable on hard, especially in rooms where you are facing multiple shotgun-armed zombies at one time and have to kill them all before you can flee. Hold your breath to "stealth" up to one zombie, wrench it to death, then hold your breath and move away until the next zombie has fired its shotgun. Rinse and repeat.

The Hard play-through was easier than my Easy play-through because I knew which enemies could be run past -- almost all of them -- and where the infinite spawn points are. The combat is very easy if you remember that the zombies are not a real threat and don't let yourself get overwhelmed.

Good luck!

An important thing to note for Hard mode is that the enemies have more health, so go for headshots as much as you can. They also do more damage, especialy the ones with shotguns. They won't turn much when they're charging up, so you can try to get behind them or to the side to avoid the shot. Later in the game, the enemies will get tougher, so it may be wiser to just run past them if possible. Bosses aren't hard since most of their attacks can be dodged with quick-time events. They'll just take longer to beat.

Also, the difficulty achievements do NOT stack, so you have to play through the game on each difficulty to get all of them. I reccomend playing on Easy first so you know what you're doing when you play on Hard.

I found the following weapons and items helped a lot with combat and survival:

-The infinite SMG. Obtainable starting at chapter 6 from Keith's first map. Keep it aimed at the head. You could probably make it with just this, but why not make it easier on yourself and get some more infinite weapons?
-The infinite shotgun. Obtainable starting at chapter 14 from Keith's second map. I saved it for the second boss, since I found the rate of fire and reload speed too slow for regular combat. The SMG works fine on him too, but I preferred the shotgun's power. Alternately, you could go with...
-The infinite magnum. Obtainable starting at chapter 8 from Willie's doghouse. You must have found all 7 bones before you run into Willie and he steals them from you. More damage than the shotgun, and obtained sooner and easier, but has a small magazine and reloads slow. Again, it should be saved for bosses.
-Keith's guitar. Obtainable starting at chapter 2 from helping Lilly at the Milk Barn three times, then going to her house's garage. It should one-hit-kill regular and armed zombies up until episode 3, then it's just two hits. Good if they're closing in and a gun would take too long. Also, it seems to miss if you move around when swinging it, but enemies attack so slow that standing still to attack shouldn't be a big issue.
-The Wesley Special. Obtainable starting at chapter 8 from giving Brian all 7 bones and going to his house. Kills wall-crawlers super quick.
-The weather doll. Obtainable from doing the Memorable Cooking questline with Emily. The ingredients for the last one aren't available until chapter 6. The doll will regenerate your health if it's right-side up when it's not raining and upside-down when it is. Your health bar will be green to show that it's working.

It also helps to have as many first aid kits as you can carry, as well as some food and drink items to stave off hunger and tiredness.