The main thing I see people doing wrong when they are having trouble in combat is not utilzing the dodge enough.

The dodge doesn't look like much, but it is borderline broken because it gives you a massive amount of i-frames where you cannot be hit by anything, even grab attacks. I almost wish the dodge wasn't in the game because it makes combat way too easy. I'd say it's almost 'fair' in hard mode.
The amount of i-frames you get decreases as difficulty increases, but there's still quite a lot in hard mode.

If you make a mistake and swing when you shouldn't, you can interrupt your own melee swing if you dodge early enough. But if you're already later than about a third through the swing, you will not be able to interrupt it.

If you memorize enemy attack patterns and animations, you should never be hit! Remember to use the dodge!!!

One last thing that doesn't fit anywhere else in this guide, while in a traversal animation, James is completely invulnerable. This includes vaulting, squeezing through a hole, or crawling through a hole. You can use this to do things such as wait out the fights in the Ruined Area, which after some time, end on their own and all the enemies automatically die.

Always wait for an enemy to attack first, then you can dodge it and attack it safely.

All enemies have counterattacks, so you cannot just spam melee and expect not to get hurt.

A 'counterattack' is when an enemy stops being staggered by your melee swings, and instead starts an attack that cannot be interrupted by melee swings, so if you keep trying to melee, you will be hit.

The chances of a counterattack increases with difficulty. Enemies that appear later in the story also have a higher chance of counterattacking.

Two hit combos are generally very safe, even on Hard combat difficulty. If you want to be super safe, you can just hit once, then dodge an attack, then hit again and repeat.

You can get free melee hits while an enemy is vaulting. However, if James is nearby, enemies can swing once as they crawl through.

If you find the game easy and you are swimming in ammo, then of course feel free to just use guns whenever you want!
If not however, then try to only use guns when you are fighting multiple enemies in a small space and there is no option to kite them, for example, through a doorway.

The pistol's accuracy focuses as you aim down the sights, no matter if you move or not. However, you have to stay still for the shotgun's and rifle's accuracy to focus, making them slightly less effective if you need to dodge a lot.

The tips below are for using the pistol. If you're using the shotgun or rifle, any hit does massive damage so there's no real deep strategies to using them.

There are three main strategies you can employ with the pistol to improve ammo efficiency and speed:
Simple, but not that effective. Leg stuns are a billion times better, do that instead.

Shooting an enemy's legs (amount of times needed increases with difficulty and with later enemies) forces it to drop to a knee, letting you follow up with a melee attack that does massive bonus damage, and knocking them down to the floor. Depending on the enemy, attacking them once or twice while on the floor will be enough to kill them.
Does massive damage, and saves a lot of ammo and time. A must for hard mode. Pistol ammo is a dime a dozen, even on hard, so you should always be going for leg stuns. On regular new game hard mode, I am able to finish with well over 100 pistol ammo even when leg stunning every enemy in my way.

As noted before, enemies may counterattack when you are in the middle of a melee combo. However, with SOME enemies (both Lying Figures and Mannequin), if you shoot them while they are trying to counterattack, it interrupts them and staggers them for a short time, allowing you to continue meleeing them safely.
This means that you can start a melee combo, then when you think they are going to counterattack, shoot them at point blank range with a pistol, then you can continue with your melee combo.
The result is what I call "The Callisto Method" because the combat loop is strangely similar to that in the Callisto Protocol, where the optimal way of fighting is weaving gunshots in between melee swings to keep the combo going.
This method is extremely useful against enemies on hard mode when you are fighting multiple enemies in a tight space and do not have time to leg stun.

Using melee
Hit it!

Using guns
Don't.

Using melee
Melee is very easy, since it's the first enemy James encounters. Its attacks are slow and very easy to dodge, but can get annoying with increased frequency and speed on hard mode. This is the only enemy in the game that you can hit with a 3-hit combo with no risk of a counterattack on normal difficulty.

Using guns
Leg stuns are great if you're surrounded and can't use melee only, and they are vulnerable to the Callisto Method.

Using melee
They have very low health, so melee is optimal. After knocked to the floor, it only takes one to two attacks depending on difficulty for it to die, just make sure to back away to dodge the AOE death effect. If you take long meleeing it while it's standing up, it might do an AOE effect, so watch out!

Using guns
Leg stuns are great if you're you're surrounded and can't use melee only, and they are vulnerable to the Callisto Method.

Using melee
You can combo less hits than Lying Figures before a large risk of a counterattack.
Semi-rarely depending on difficulty, mannequins will do a special move where they dodge one of your swings, and go into an uninterruptible (by melee) attack that you must then dodge. If you do this, it opens it up to additional hits.

Using guns
They are very susceptible to leg stuns, and using the Callisto Method.

Using melee
Always use melee if you really want to kill them. They die very fast to melee. They are harmless most of the time and take ages to attack, preferring to just run around on the walls doing nothing. You should ignore them until you hear the extremely obvious and loud soundcue of them starting an attack (strange comparison, but it kind of sounds like when you shoot a weakpoint on a headcrab zombie in Half Life Alyx), then dodge which will make them fall on the ground next to you for easy melee hits. They have almost no health, even on hard difficulty.

Using guns
There is no reason you should use guns against them. They are so skittish that you can just ignore them if they are in gun range, and if they are not in gun range, you can just melee them and they die extremely fast.

Both Nurse types freeze at random intervals while their head shakes. You can use this time to attack them freely.
Using melee
Melee should not be a problem unless you are surrounded.
They sometimes like to delay their swings, so be patient and wait for the swing to dodge.

Using guns
They are more resistant to leg stuns than mannequins, and pistol gunshots do not stagger them unless it is in the legs so the Callisto Method does not work very well on them. Since nurses have a lot of health, you should be going for leg stuns.

Using melee
Their attacks start suddenly and are very fast, but melee is still a viable method when one on one. They often try three-swipe combos with their knives or a two-swipe combo with a grab.

Using guns
They are also more resistant to leg stuns and pistol gunshots do not stagger them unless it is in the legs. They have a lot of health, always go for leg stuns.

Listen for their soundcues. Whenever they attack, they make three distinct short 'viper hissing' sounds. On the third sound, that is when the attack is actually going to happen, so just wait until you hear the first two, then dodge on the third and the i-frames will protect you. Visually, the tongue comes up through the floor on the second hiss, then stabs at James on the third.
Using melee
Don't. If you want to save ammo, just avoid them and run past them, even the boss Mandarin. There is no reason why you should ever waste time meleeing a Mandarin. Either shoot it, or just ignore it. There is no advantage to meleeing it; if you want to save ammo then avoid them, if you want to save time then shoot them. There is not a single time in the game where you HAVE to kill a Mandarin.

Using guns
It's better to just run by / ignore them, but if you REALLY want to kill it (you can just wait out the timer in the Ruined Area to avoid fighting the Mandarin there), then you can shoot the "lips" it's hanging onto the floor with. If you do enough damage, it will let go, and if you do enough damage fast enough to the other one, it will fall into the abyss.