If we are gonna talk about the hardest parts on Hardcore. Sections 3 and 4 of the first Marine Mission are the most difficult. Mainly cus you only have the pulse rifle and shotgun at that point. The fact that you know where the aliens will spawn helps but there is a part near the end of Section 3 of Mission 1 after you open a door that aliens will come from both sides, you need be very fast cus you can be swarmed so quicky there won't be enough time to kill them all in time.
On the Predator fight you can be one shooted by the plasma or spear slash depending on how much HP and Armor you have, its easy to die and the Predator is a bullet/rocket sponge but for plasma you can just use cover and since you are faster than the Predator you just need to move backwards for him to not hit you with the spear.
Praetorians can be hard if you don't use the minigun, on the last part of the last Marine mission when multiple Praetorians come to you I prefer using the Sniper rifle instead, can be risky if they come too close.
For Predator campaign the first Praetorian fight on the first mission is the hardest part, same reason as the first marine mission, you don't have the best weapons to fight that thing on Hardcore. I just shoot all of my speargun and try to jump backwards while swinging my spear at that majestic Praetorian until its dead so I can take his head. That thing can kill you in 2-3 second with its claws. Goddamn hardest boss in the game is a Praetorian on the first mission. Yay.
The Queen is so slow I can bitch slap her with the spear to death without getting a single hit. The 2 Predalien fight on Mission 5 can be hard depending on what weapons you decide to use, same as in Praetorian if you they come too close you can die really fast. The last section of Mission 5 can be hard cus you need to deal with a Praetorian and a swarm of aliens so even with plasma spamming if your energy runs out you are screwed but it can be avoided by entering a passage the Praetorian can't get in. Rykov on the Exosuit can one shot kill you but pistol secondary fire gives a easy win.
For Alien Campaign, Androids with minigun can pretty much one shot kill you and you can't stun them with tail or headbite right away like you do with humans. You need to claws them to death fast before they have a chance to start the gun. The last fight against 2 Predators is hard mainly cus if you jump on the platform and the Light Predator happens to have the plasma caster equipped there isn't time to avoid it as it follows you and its a one shot kill.
Primal Hunt is absolutely broken in Hardcore. Corporate and Predator you have to deal with such a huge swarm of enemies that your only option is the one shot kill flamethrower for drones/runners while saving minigun ammo for Praetorians as Corporate, and plasma spamming caster and pistol as Predator. Trying to fight 2 aliens with melee as Predator is already a challenge. I like trying to use melee but after every fight you need to heal and recharge, kind of gets boring. Also last Corporate mission, they give you only pistols, shotgun, pulse rifle to deal with all of that. That part where you need to wait for the elevator and a Praetorian with a swarm of aliens come... they didn't test that shit, its a nightmare.
As Predalien, sentries and droids are the worse, but you can die so easily from almost anything, need to spam the stun tail attack on anything you see so they don't get a chance to shot you.
And people think the AVP2010 or Isolation are hard. I didn't have much trouble with AVP Classic, Concrete Jungle... Extinction can be hard and frustating in some parts. ACM with Templar V6 might come close to Primal Hunt's hardcore, tested it in coop with some people and even with 4 people it was hard, the no hud thing is a bother and the Lurkers were taking over a full pulse rifle clip to kill lol. The DLC was already a nightmare on V5 cus Gearbox had already made it harder than the main campaign after people complained about the game being easy, and that stacks up with all the buffs Templar gave to the Aliens.