A recent update added a track for the Chained Court, Rage. It certainly fits, as you'll either be ripping and tearing through multiple weak enemies, or getting your own huge guts ripped and teared if you completed Hell's Arena.
If one did not complete Hell's Arena, the Chained Court. It starts you out in a room with a Chainsaw and four berserk packs, and the only opposition are 20 Former Humans (10 can be Former Sergeants or Captains on high difficulties, though you'll still easily plow through them with the berserks), and two groups of two Cacodemons/Hell Knights/Hell Barons (depends on difficulty), that are sealed away and only have to be confronted if you choose so. If you did complete Hell's Arena, the level layout changes to approach a Brutal Bonus Level, with two of the berserks not being there, the zombies being focused on one side (instead of being evenly split), the stronger monsters being right outside the room you start out in instead of being sealed away in a distant room they can't escape, and there now being a boss that can easily slaughter the player at their low level, due to him being a freakin' Arch-Vile.
Hell's Armory, if not on Ultra Violent/Nightmare. The only high level threat are two Arachnotrons, and the level has many places to corner shoot from, while having a long 1 tile wide hallway to chokehold enemies. There is a boss you must kill to get the level's full reward, though this boss is easier than the previous bosses you fought, and easier than the bosses to come, regardless of the build you use. The rewards for the level are also quite large, even if you choose not to fight the boss (and if you do fight him it includes the only guaranteed rare mod pack in the game). The only healing item being a hidden Supercharge that you have to travel through lava to get can keep this from being a breather level, if you don't use the many opportunities to corner shoot and soak up damage.
Halls of Carnage pre-0.9.9.7, a straight forward level whose gimmick is that it has a lava flood that will overrun the player if they're too slow. However, the lava flood is pretty slow, and even a poor player getting repeatedly knocked back the Sergeants in the beginning will make it to the end with time to spare. Besides that, the only other parts of concern are the locked doors in the middle (which will only be a potential problem for new players), and the small maze at the end filled with some strong enemies (which isn't much of a threat due to the many corner shooting opportunities). What really makes the level a breather though, are that there are three Supercharges in your path to the stairs (one right in the beginning, one in the midway point, and one in the end), which should prevent any player from having to expend any medkits on the level to complete it. Plus, there's a guaranteed BFG (one of two in the game) at the end of the level, and any build will get through the level easily.
Halls of Carnage is not as much of a breather level anymore in version 0.9.9.7 however, where not only does the lava flood faster (up to a ridiculous rate of a column every 2 seconds on Nightmare! difficulty), the first two Supercharges were replaced with Large Health Globes, and the third Supercharge was removed with nothing to replace it.
For those running Shotgun builds, the City of Skulls can be one, as Shotguns tear through Lost Souls and excel at fighting large groups of weak enemies (the only concern Shotgun builds will have here is the rather sizable expenditure of ammo). If you have Vampyre and some form of indestructible armor it's even easier, except for a tight spot right at the beginning.
For those running melee builds, the Unholy Cathedral, as a moderately sized group of Lost Souls and Demons are little threat to a melee build at this point in the game, and even the incredibly powerful Angel of Death is no match for a melee build that's berserked.
Breather Boss: If you have the Dodgemaster trait and know how to utilise it, the Cyberdemon can be rendered this, as you have a guaranteed way of dodging its rockets, while you can attack it freely between its reloads. If he hits you even once it was probably a cheap shot before you could see him. Coming into the battle with fireproof Red Armor, which is easily obtainable by this point, also greatly nerfs the threat of the Cyberdemon. Finally, a melee build capable of Berserking and a solid piece of armor can just tank the first hit, go berserk, then just close in and tear him apart.
As noted above, if your character build is fully tailored towards melee the Angel of Death is barely a speed bump.
As known by the DoomRL community, the VMR (Archviles, Mancubi, and Revenants). Archviles have the most HP of any non-boss and non-nightmare monster, are one of the fastest monsters, have a very powerful attack that can only be dodged if your speed is fast enough, and most importantly, are capable of fully reviving any dead monster in their sight. Mancubi have very high HP and high natural armor, and have the deadliest attack of any monster in the game (which consists of them firing three rockets that individually deal very high damage, and have a large splash radius that can result in you getting hit by all three if you're near a wall, resulting in extreme damage if not an instant kill), though they are hindered by their extremely low speed and being easy to corner shoot. Revenants, while not having as high of HP as the other high tier monsters, are fast and shoot a powerful projectile with a splash radius that aims at the tile the player was standing on, which results in their attack never missing. The threat of the VMR can be easily nerfed though, as they all deal fire damage in their projectile attack, and fire damage is very easy to gain resistance to (a simple fireproof armor assembly on Red Armor will give the player a Red Armor with 55% fire resistance, which can even make the full brunt of a Mancubi blast easily brushed off). There's also the Fireangel perk if you really, really, really hate these guys, which makes you completely immune to splash damage, nerfing them even more at the cost of other master perks.
Arachnotrons, which while lacking any special traits, are fast, have high HP and armor, and have a rapid fire weapon that can deal high plasma damage and is difficult to dodge all the blasts. Fortunately for the player, Arachnotrons are extremely weak in melee (having a weak melee attack and taking 100% more damage from melee attacks), which can be enough to keep them from being demonic spiders.
The nightmare versions of Archviles and Arachnotrons. The original versions were already capable of being demonic spiders by themselves; the nightmare versions have substantially more HP, speed, and even stronger attacks. Nightmare Arachnotrons additionally do not have the double melee damage penalty normal Arachnotrons have, and can fire at a player in melee range with their deadly Plasma Rifles instead of attacking with their pitiful melee attack, thus eliminating the main weakness that kept normal Arachnotrons in check.
Barons of Hell can also qualify. While their HP isn't as outstanding as it was in the original Doom (in DoomRL, their HP and armor values are equivalent to Mancubi), and their attacks aren't as dangerous as the attacks from the monsters above, they have two unique traits that make them a huge threat to your survival. The first trait is that they're the only monster whose projectile deals acid damage (besides the Bruiser Brothers, which are a boss form of Barons). Acid damage is by far the most difficult type to obtain resistance to (unlike the fire damage from the VMR), and acid deals double damage to your armor (just two hits from a Baron is enough to possibly bring Red Armor from full to below 50% durability). As such, Barons will nearly always hit you hard, and will brutalise your armor (which in turn, softens you up for them and the other demonic spiders). The other trait Barons have are that they are able to pick up and wear armor themselves, as well as pick up and use healing items, which has a twofold effect. Combined with their already high HP and natural armor, an armored Baron can take a ridiculous amount of hits to kill. And when you bring a Baron to near death, they can use a large medkit and bring themselves back up to full health instantly. Besides this making them being capable of taking even more hits to kill, it deprives you of armor you may need (you can get the armor they wear when you kill them, though the armor would be severely damage if not destroyed), and of the medkits that are vital to survival. Overall, while they may not provide the immediate threat the other demonic spiders do, they provide a greater threat to your long term survival, and a bad encounter with them can cripple your chances of ultimately winning even if you survived the encounter.
Game Breaker: In past versions the Ammochain master trait gave you infinite ammo for rapid fire weapons (even removing the need to stop and reload), letting you spray plasma fire everywhere just in case there might be an enemy past your range of vision. Plus not having to carry any ammo meant carrying a lot more medkits, phase devices and the like. The only catch is that rapid fire weapons aren't all that useful unless you either have the Eagle Eye trait(which you can't get if you want Ammochain), or agility mods(which were rare random drops at that point).
Ammochain was nerfed in 0.9.9.4, slightly. Now it uses one ammo. Per burst. It wasn't that much of a nerf, but you can't just fire blindly every step of the way and you do need a space or two reserved for ammo again.
Unless of course you have the Nuclear Plasma Rifle, which has infinitely self-recharging ammo in exchange for a small clip and inability to manually reload. That "small clip" still means twenty four consecutive turns of rapid fire with ammochain.
Mods (including agility ones) are much more common as of the newest version, which predictably makes Ammochain more powerful. This change seems to affect other weapons just as much, however.
Tacking the Sniper mod onto a Plasma Rifle - especially if you have Ammochain - can make a good portion of the game a cakewalk. Guaranteed hits with a weapon that is only balanced by its sheer inaccuracy makes for piles upon piles of dead Barons of Hell. In addition to this, you can simply fire blind and be guaranteed to kill something if there is, indeed, something in the way of your firing line.
Genius Bonus: "You hear the trumpets of Jericho in the distance..." is one of the messages you can get at the start of a floor. Some knowledge of The Bible can let you guess what this means...there's a lever somewhere that'll knock all the walls down.
Goddamned Bats: Lost Souls pre-0.9.9.7; they have ridiculously high speed (with 220% speed, they're by far the fastest enemies, and can get 2 to 3 moves for every move the player has at base speed), and can quickly swarm the player, inhibiting the player's movement and distracting them from other enemies. They're even worse for pistol users and chain gunners, as they have a massive 50% bullet resistance and can take many hits from these weapons before dying. 0.9.9.7 adjusted their AI; instead of behaving like a normal melee enemy who happens to be ridiculously fast, they now behave like their normal Doom counterparts, where they wander around at a slow speed, and then charge at the player in a straight line at their ridiculous speed until they hit something or are hit. This AI change made them a lot less obnoxious and not as much the threat they were in swarms, but they are still very annoying.
Former Sergeants can be this. Since they use Shotguns, they'll never miss the player, and they'll keep knocking back the player with their attack, which is especially annoying for melee builds. Their extremely low HP and shrapnel damage being double reduced by armor keeps them from being real threats to the player beyond the very early game.
Good Bad Bugs: In the Angel of Marksmanship or Shotgunnery challenges, you can't use any weapons except pistols or shotguns, respectively, but can still attack with the Emergency Weapon of your fists. In some versions, when you attack with a melee weapon wielded, it will cancel the attack and the use of time it would have taken, then go ahead and punch the monster anyway. You could kill anything by revving up a chainsaw and then punching them a few dozen times in an instant.
That One Level: The first boss level, Phobos Anomaly, ironically even moreso on the Hey Not Too Rough and Hurt Me Plenty difficultes, rather than the hardest difficulties. On these difficulties, the ambush in the beginning consists mostly of Lost Souls, who'll surround the player unless (or more likely even if) they immediately run for the beginning or right area. If the player does not run and tries fighting them in the open, the player will either die, or be left severely weakened while still having the Bruiser Brothers to fight. This area is an even bigger obstacle for those running pistol and rapid fire builds, due to the Lost Souls' extreme bullet resistance. For these players, getting lucky with a Phase Device to teleport them past the ambush is pretty much the only somewhat reliable way to get past this part without sustaining heavy damage.
Among randomly generated levels, Arachnotron caves are notorious. Caves are small open levels, with barely any cover, and consist of a single enemy type. In Arachnotron caves, you often start with multiple Arachnotrons around you in your line of sight, with even more not that far away. With barely any cover (which is vital for avoiding Arachnotron fire), you have little protection from their plasma volleys, it's difficult to approach them to exploit their extreme melee weakness, and you can't run away unless the stairs are nearby. Arachnotron caves are also not uncommon in deeper levels, and on higher difficulties, you're about guaranteed to run into at least one.
Unwinnable by Insanity: In the The Wall, it's possible to get past the wall without blowing a hole through it, by getting lucky with a Phase device and teleporting past it. If the player did this on a challenge that restricts their weapon use (thus preventing use of the Rocket Launcher and Missile Launcher), or without having a Rocket Launcher (and then lets the guaranteed Missile Launcher get destroyed before picking it up) with enough ammo to blow a hole through the wall (despite there being plenty of free rockets on that side), they can get permanently stuck behind the wall if they did not have another Phase device or a Homing Phase to teleport them back out. A player would have to be intentionally invoking this though, or have extremely bad judgment, to use their only Phase device to get the past the wall when they have no guaranteed way of getting back out.
In general, a player with a nuke can make the game unwinnable at about any time, by activating the nuke when they're not invulnerable (nor have a source of invulnerability nearby), while more than 10 seconds away from the stairs to the next level. The exception to this would be the final level, where nuking the final boss and yourself nets you a "partial win". Granted, you can still quite easily get to a game over from this state, unlike the above.