Hard difficulty in this game isn't very hard, just frustrating at points. I would recommend playing this difficulty first, since the easier playthroughs will seem much, much easier after playing through this difficulty.
1. Save a lot. Like every 2 minutes. And save on multiple save slots, in case you get stuck on one save. This game has the worst save system ever. Every time you die, you go back to you're last save. I remember very vividly when I died the first time and had to do the entire first act over again.
2. Use cover wisely. Although you can use cover, sometimes you can get a better shot by not using cover and just standing behind the wall or object.
3. Advance slowly. Many times in the game, if you advance too quickly, more enemies will spawn and kill you very quickly.
4. Take breaks. This game is infuriating when you get to a part you can't beat due to horrible controls, no ammo, or lack of health due to a bad save. I blitzed though this game in 4 days and wanted to throw myself off a cliff when I was done.
In the first act, the second monk with a shield can be tough. Just hide behind the stone pillar and unload on him with infernal shot SMG when he comes out. Also, the last part with the red walls coming at you gave me a lot of trouble. Charge them right away and shoot them. As soon as there is only one in between you, roll through.
In the second act, there really wasn't any particularly hard parts that stick out. Just make sure to use cover well and when you can get on a turret to kill enemies quickly. At the boss fight at the end, just shoot the generator things with an infernal shot and head shot the zombie things for mana.
The third act wasn't all that hard either. I was caught up trying to blow up the boats for a while until I found you could skip them. The last part where you are hurrying to the train was a bit tough if you don't take some time to concentrate on not falling off a ledge.
Act four had a couple hard parts. This is the act that the soldiers that can turn invisible appear. The only strategy that I came up with was to hide until they became solid again and shoot. Repeat if they decide to go invisible again. The part on the ship where you have to kill the robot things isn't too hard if you know what to do. Lead them on paths through the boxes that have explosive barrels and shoot the barrels as they pass. Not much to say about the boss on this act. Just pick up the rocket and shoot him a lot. Make sure when fighting him to stay away from Barbara, or she'll die and you have to start from your last save.
Act five is very easy until you get to the last valley before the observatory. When you get to the valley with all the big turrets and soldiers, wait around the corner and kills the soldiers that spawn and then take out one of the turrets. Advance a little and then repeat when new soldiers spawn. The end boss fights are pretty easy. The first end boss fight is just like the one at the end of act two. Kill the flying guys to get mana and then shoot the generators with infernal shot. Then shoot him with infernal shot until he dies. For the second end boss, just shoot him with the energy rifle until he goes to his knees and then activate the yellow terminal, then activate the big ball of doom. Repeat three times and the boss goes down.
After you beat the game on hard, prepare for another 2 playthoughs, since the difficulties don't stack. Medium and easy are pushover difficulties compared to hard though.