Mine was the construction truck on Chapter 3 on Nightmare. I lost twenty or more times on it. The randomness of the attacks of the Taken combined with the time it took to destroy the truck took me forever to beat. Hardest part in the game... 

And what about you?    

" Some part in a barn where you had to jump over a fence and then you get jumped by loads of the massive ones. I just had to try to run past them and to get to a light because I couldn't defeat them. "

for me it was episode 6 crossing that damn bridge! i died like 20 times before even getting to the crane because of the pieces of bridge would fall out while trying to dodge the dumb flying objects.

The hardest part for me was at some point i dont remember when but you only had a flashlight and no weapon so all i could do was run. 

I never really ran into any trouble during the game on Hard. I always had way too much ammo to be in too much danger. Even versus the construction equipment I always found that if I was in trouble I could just drop a flare and be safe.

I played the game on normal and didn't run into too many sections that involved me dieing a lot, but the whole last episode was pretty hard. 
I actually feel the game's difficulty was pretty spot-on throughout, I was always feeling challenged and at the edge of my seat, but didn't ever really find myself frustrated or constantly restarting the game.

I actually had a lot of trouble with the part on the dam or bridge, can't remember which it was, when you are trying to get to the well lit room I don't even know how many times a part of the floor fell as soon as I stepped on it. Never really had trouble with the enemies since I would just let my flashlight recharge instead of wasting batteries.

Hardest part for me was figuring out where to go next a few times during the game.  Just remeber walking around.  In both cases (forget the episodes) it was a ladder I needed to find, but it took a few minutes of wandering.  That was proabably the only thing I was ever frustrated with in the game.  There were hard fights, but nothing terribly frustrating or controller-smash inducing.  What a great game.

I never thought the game was to hard, I thought the difficulty was just fine, although I don't know about nightmare mode.  I mean the game gave you so much supplies I couldn't even use them all, which I actually liked.  It was fun, and a change being able to use the powerful weapons so much when most games will give you like one rocket launcher through the entire game.  
 
I guess the hardest part though was when you had to run through a section of forest with only a flashlight and no gun, and you get ambushed buy a ton of enemies, I died two or three times during that part.
 
Also on the construction truck part I didn't fight it, I just opened the gate and ran past it.