And while it didn't contain any content on the level of the above example, the official sequel, DOOM II: Hell on Earth is noticeably harder than the original's "standard" episodes. Imagine what playing "Nightmare" on that game must be like...
The Plutonia Experiment official expansion for Doom II spawned an incredibly difficult subset of Doom levels that emphasizes combat against vast hordes of monsters, often dozens at a time. Levels have been made with literally thousands of enemies, often with fights against multiple "Arch-Viles" - powerful enemies who revive other monsters and have a delayed line-of-sight attack which can take off 80% or more of the player's health.
While Plutonia may have significantly upped the difficulty level compared to the previous installments, it was the user-created map set of Hell Revealed that brought about gigantic monster hordes. In fact, such maps are said to have "Hell Revealed" style gameplay within the community. In particular, Hell Revealed's 24th level, "Post Mortem," has so many monsters (over 500!) that it's impossible to save your game on it, unless you're using a source port of the game. And then you have Hell Revealed 2's super-secret level, "Playground," which has over 1,600 monsters. Even on the lowest difficulty, this map will likely cause you to tear your hair out many times over. And let's not EVEN get started on MAP31.note That's if you can even run the God-damn level. Even with the newest version of ZDoom, GZDoom, or Skulltag (which have significantly improved renderers compared to the original), the sheer amount of demons will make your computer chug.
Since Hell Revealed, the "HR" style of gameplay involving huge, intensely difficult fights has become a staple of Doom mods. One of the most famous levels ever, NUTS, is nothing but two huge rooms with over 10,000 monsters. It's infamous for getting around 1FPS on the vast majority of computers and source ports. Sunder is a good choice for the most difficult serious map set ever created. Most of the levels are unbeatable without cheats, yet the entire thing was (according to the author) playtested and balanced.
The Brutal Doom mod tweaks enemy behavior to make them smarter, stronger and more aggressive (Cacodemons can strafe quickly to dodge projeciles, Imps have faster fireballs and have a leaping slash melee attack, Cyberdemons fire five rockets instead of three, Spectres are completely invisible except for their eyes, only becoming visible when they attack.) Reloading is also added, now requiring the player to monitor how full their magazines are so they don't get caught reloading at a crucial moment. Though there are some things to help make it easier as well. On top of added secondary fire for most weapons, Berserk packs now allow the player to make executions which, on top of being bloody and ultraviolent, render the player immune to damage for the duration and restore health, and the dinky pistol is replaced with a far more useful assault rifle. That doesn't mean the enemies get the same perks, like a Imp tearing you apart.
Speaking of Brutal Doom, the Brutal Doom Starter Pack is a map series by the original mod creator specifically designed for this mod. It just as difficult (and awesome) as it sounds, particularly the last episode with suped-up boss monsters and hordes of enemies around literally every corner.
Doom (2016) starts manageable, but goes to its roots and spikes the difficulty up tremendously in the later areas, particularly when the stronger demons start showing up. To scale up with your upgrades and weaponry, rooms (even the small ones which are impossible to maneuver through) are often filled with near Serious Sam levels of enemies with different types mixed in to obliterate you when you're not looking. All of the old demon roster has Taken A Level In Badass too.
The original Red Faction turned from challenging to nightmarish about 2/3 through the game. The introduction of heavy machine gun wielding mooks and instant death wall-penetrating sniper railguns mooks made the game a painful affair.
It may not seem evident early on in the game, but as the difficulty spikes, you WILL notice that the enemies even cheat. They know when you are reloading, and will rush you when you try to do so.
Red Faction: Armageddon is a Third-Person Shooter, and for the most part is rather straightforward to finish. However, it takes inspiration from the original by dialing up the difficulty Up to Eleven in the climax. The bugs respawn like crazy, there's little environment to destroy in the tight underground corridors, and the checkpoints are few and far between. Moreover, as you're approaching the Queen, Behemoths (which only one served as a separate boss) blockade your way, forcing you to deal with them and the virtually limitless enemies. When fans say the Final Boss that follows is a Breather Level in comparison, you know the difficulty of the final few levels is going to be bad.
Tactical FPS/mil-simOperation Flashpoint is... unforgiving, to say the least. You can generally take no more damage than your enemies can (two or three shots is usually all it takes), and most combat takes place out in open countryside where ranges are long and there's little cover. Missions often last longer than 15 minutes, but you can only save once per mission (in addition to the automatic checkpoints). One particularly maddening mission starts with you in the forest (alone, your entire squad having been killed off), from where you have to make it a kilometer and a half through enemy territory, dodging enemy patrols, a helicopter, and the occasional tank to get to the extraction point, which then gets overrun just before you get there. Then you're taken prisoner.
The Resistance campaign from the expansion pack of the same name is even more difficult. At least in the Cold War Crisis campaign you're fighting as part of an organized army, with tanks, air support and so on, but in Resistance you become the leader of a poorly-equipped band of guerrillas. Your weapon supply must be restocked by collecting weapons in the battlefield, and guerrillas killed do not re-appear in following missions. At least it simulates those who have to hide out in the mountains to survive and steal equipment from the better-trained and equipped enemy.
And don't even talk about the Red Hammer campaign, which is truly Nintendo Hard and at one point contained a bug that made it impossible to finish it at all. The final patch for the game, which actually renamed the game to ARMA: Cold War Assault, also removed this campaign.
The Serious Sam franchise is well known for incorporating classic gaming elements into a more modern setting, including sheer fucking nightmarish difficulty. You will probably die more times in one Serious Sam game than in all other FPS games you've played combined. Even on "Normal" mode, the games still qualify for this trope. Thankfully, the extreme difficulty generally comes in waves.
Faceball 2000 (the SNES port) gets difficult once you begin to meet drones that begin to fight back competently (e.g. Wallys, Rovers, maybe Turkeys) starting from the second world. At this point, you probably still don't have enough armor pickups to deal with large numbers of enemies. The end game gets ridiculously hard, as groups of powerful drones can swarm you without warning (e.g. Ninjas, Sharks) and make quick work of you.
Metro 2033, which comes from the same lineage as S.T.A.L.K.E.R. below, definitely shows this. Your character isn't a badass, or a stalker, or a soldier; you're just a 20 year old kid trying to make a trip across nuked Moscow, running right into the paths of mutants, Nazis, Communists, bandits, anomalies, and everything else that could redecorate its part of the station platform with your face. It's not too hard on Easy or Normal modes, but put on Hardcore, or any of the Ranger difficulties, and you get to see how you'd actually fare in a real life After the End survival combat environment when you don't know the places, don't speak the language, and ammo is so valuable and scarce that it's used as money! How will you do? If you're lucky, there'll be a corpse, or at least a red smear for the rats...
Command & Conquer: Renegade. Gameplay is largely a loving throwback to older-style first person shooters, meaning lots of elite enemies constantly attack. There are lots of annoying respawning enemies and a majority enemies are Demonic Spiders. Levels are also very long and large, and there is no auto save or checkpoint system.
Rise of the Triad is no slouch in the difficulty department. Most levels are difficult, and not just from the abundance of enemies. There are plenty of traps to worry about, maze-like level design (fortunately the auto-map in single-player helps make this aspect of the game a bit easier to handle), and then there's The NME...
Perfect Dark, bonus points for being an actual Nintendo game. As first person shooters with complex mission objectives and use of stealth were still relatively new at the time, figuring out just how to complete each mission was hard enough. Doing so without being seen made it harder. And thanks to taking away the Mercy Invincibility in its spiritual predecessor GoldenEye (1997), every enemy was a potential Demonic Spider.
Descent: The unique zero-gravity, floating mechanic made the game harder to learn than most first-person shooters as it is, but the real difficulty comes from the brutally unforgiving enemies. Drillers (hitscan weapons) and Heavy Hulks (homing missiles) are absurdly common enemies that do insane amounts of damage and have huge accuracy, even on low difficulty levels. On the higher difficulty levels, even the easiest enemies are capable of ripping you apart in a matter of seconds due to their shots firing being stronger, faster, shooting more bullets per volley and healing items recovering less as the difficulty gets higher. The Insane difficulty level is very appropriately named.
Duke Nukem Forever has been criticized for this. It qualifies on numerous levels: very limited health and thus the ability to be killed with only a couple of direct hits; an overload of monsters in certain areas; limited ammo; and ambush attacks.
Of course, all that ends up moot once you manage to max out your Ego, where then you can take as much damage as you could in Duke Nukem 3D with Regenerating Health to boot.
The games were deliberately designed to be as tough as possible, and subvert and deconstruct dozens of common FPS tropes. Remember those other FPSes where you had limitless supplies of ammo which took up no room in your magic bottomless bag? No. Remember those games where the people not shooting you spoke the same language as you? Nyet. Remember those games where there'd be some guy who would helpfully fill you in on the boss's weak point before you fought him? Nein. Remember those games where you didn't have to eat, where being injured was just a reason to be slightly more cautious, and you could heal by simply walking away and waiting for a bit? Non. These games want you dead, and a lot of content was Dummied Out in the first game and the AI's capability scaled back because it was regarded as too unfair. Most mods restore a lot of it with the express purpose of making the games even harder. With those enabled, it's not so much about shooting as it is outmaneuvering the enemies that will get you to win fights. Yes, even with mutants.
There's a very good reason the series is sometimes retrospectively called "the Dark Souls of First Person Shooters", with allthatentails. There's also a good reason why a common word of advice to new players is to bind Quicksave and Quickload to the mouse buttons.
Brothers in Arms qualifies, especially on harder difficulties. Your weapons are realistically accurate, which means they have a limited effective range, you can't take much damaged and the AI is both intelligent and accurate. The only effective way to take on more than one enemy at a time is to suppress and then flank them, but be careful, because there's often more than one group of enemies around, so they're trying to do the same thing to you, and if you catch a stray round while moving, that's it. The endgame, where all the enemies are armed with the accurate and powerful STG 44 Assault Rifle, is downright murderous if you make a mistake.
Blood has even the weakest of mooks dealing huge amounts of damage even on lower difficulties (along with being rather stingy on the health pickups,) and the weakest ranged weapon in the game (which you'll be stuck with for a while) deals continuous damage, but still takes a while to kill anybody, requiring you to either unload more shots into the enemy (in a beginning where ammo is sparse) or just shoot once and run away until they die.
Quarantine has every vehicular mook not in a passive state a Demonic Spider in every level (including the first map), and even the pedestrians who are hostile are annoying Goddamned Bats. Armor is pretty much required to complete any mission in the levels you're in, because the unpredictability of the Mooks gets frustrating for a while, and even then, armor here in this game skirts dangerously close to Armor Is Useless thanks to the Mooks having unfairly powerful attacks. Not only that, everything else tries its level best to slaughter you in the city of KEMO with even the traps and walled defenses harming you. Just to let you know, whenever you pick up a passenger, every single mission is a Timed Mission and depending on the location you're in, you could end up with a frustratingly short timer before you could complete your mission, and to worsen matters, the city's layout is maddeningly confusing if you don't check your map. Justified, since you're driving a futuristic, hover-capable weaponized taxi car and making money by gaining fares. Also, the fares are randomized whenever you pick up a passenger, which can range from a fat paycheck that is good enough to buy you some more ammo and new weaponry/armor to a dirt-poor wage that isn't enough to buy a few items from the grocery store (of course, this is just a hyperbole, since there is no ability to get out of your vehicle in the game whatsoever). There are hardly any safe spots to rest in, no difficulty level to choose, and Save Scumming is pretty much required to complete the game.
Nosferatu The Wrath Of Malachi: Between the limited supplies, hordes of difficult enemies popping out of every shadow and hiding place, lengthy levels, and the fact that you can lose family members if you take too long, which loses you items and makes the final boss harder, you've got yourselves one hella tricky shooter.
While the trilogy is difficult in general thanks to its GoldenEye roots, trying to get Gold on the Challenges (and some of the more notorious Arcade League matches *coughCan'tHandleThiscough*) can be hair-pullingly frustrating.
Tower of Guns is a short roguelike shooter designed to be beaten in about an hour, but delves straight into Bullet Hell, and doesn't let up; your weapon also gets weaker the more you get hit. Good luck getting to the Final Boss without the "I'm too young to die" perk, and beating the boss WITH the perk.
Lovely Planet combines One-Hit-Point Wonder status with tricky platforming and an instant-kill hazard should you not disarm it. And you don't have a sight, you have to aim purely by feel. It says something that the game gives a tutorial for the respawn button.