Big-Lipped Alligator Moment: In the same room as Clayface is a prisoner who doesn't seem to be any recognizable Batman villain and his model is too detailed to just be a random NPC. It's the winner of the "Appear in the game!" contest's appearance—but the average player isn't gonna know that.
Breather Boss: Combined with Anti-Climax Boss. The very first boss encounter (with a random mook who was exposed to a prototype version of Titan) seems like it'll be a fair challenge... but he suddenly dies from heart failure after a fairly brief amount of time, no defeat necessary.
The Scarecrow segments. Some consider them to be among the best scenes in the game, while others argue that they're not actually scary, take way too long and only distract from the story and regular gameplay. There's a third camp that likes the Mind Screw parts but dislikes the sidescroller gameplay.
Batman's confrontation with Killer Croc. If it works for you, Croc's lair is a tense slog through a Nightmare Fuel factory; if it doesn't, it's just tedious.
Rain in the remaster. Some feel that it's completely unnecessary and ruins the athmosphere, while others feel like it adds some life to the barren overworld, looks better, and adds consistency in the game's schizophrenic weather. Explanation It's raining in the intro, it's not raining during gameplay, yet it's raining when Batman is in the sanitarium.
Counterpart Comparison: A lot of people who have played the game a few years after its release have noticed a coincidental resemblance◊ between Arkham Asylum's high-security henchmen and Bane in The Dark Knight Rises. Inverted, as the incarnation of Bane in The Dark Knight Rises is the more recognizable of the two despite making his first appearance a few years later.
Crazy Awesome: Joker in a nutshell, when playing as him. The guy can leapfrog over attackers, he uses a joy-buzzer and a comical eye-poke in combat and can use chattering teeth bombs in his predator challenges, yet he can still be as badass as Batman.
Creepy Awesome: Scarecrow full-stop. This guy has some of the most genuinely scariest moments in the game, is a rather challenging boss, and has an intriguing amount of character that hides much more sinister evil within him.
Demonic Spiders: Gun-wielding mooks, knife-wielding mooks, and Ivy's plants.
Draco in Leather Pants: The Scarecrow has got himself a few fangirls. Might have something to do with him being shirtless for this game.
Evil Is Cool: Being a Batman game, it's only natural that his amazing cast of villains would become some of the most memorable moments and encounters in the story.
Foe Yay: Batman and Poison Ivy have a lot of this throughout the game. Although it's debatable since Ivy is The Vamp, she comes off as very interested in the dark knight and even has Orgasmic Combat with him.
Poison Ivy: Are you ready for me? Do you think you can handle me?
The Captain America: Super Soldier game copies this game's basic fighting engine (though not quite as well), with a counter, dodge, stun, and attack button. It also tries to copy the Metroidvania style layout, but to less success. Still, imitation is the sincerest form of flattery...
The movie-licensed game based on The Amazing Spider-Man 2012 film goes further in copying Arkham Asylum. In addition to having the same combat system as Arkham Asylum, there are also patient interview tapes (redubbed "audio evidence tapes") and a level where Spider-Man rescues doctors from escaped patients in an asylum. The devs openly admit they used Arkham Asylum's combat because they felt it was a good fit for Spider-Man.
Middle-earth: Shadow of Mordor drew its combat from the Arkham games, and they also sought to make a licensed product entirely separate from the movies and more suited to the videogame medium, which they saw Arkham Asylum as an example of it being done right.
Game Breaker: The Batclaw in Predator rooms. A single use of the Batclaw on a mook next to a railing will result in an automatic takedown, as the mook is pulled over the railing and falls to the ground. This removes the risk of Batman being spotted and getting shot at due to the range of the Batclaw's rope. All of the Predator rooms from the point where you acquire the Batclaw have such railings. The Ultra Batclaw will allow you to pull up to 3 mooks for an instant takedown, but there's only one predator room left in the story when you get it so it doesn't get to be as useful outside the Challenge Mode.
The mooks with stun batons that appear about a quarter of the way into the game. If you don't deal with them promptly and correctly, their batons can quickly whittle your health down to half on the intermediate to higher difficulties.
Arkham Inmates in the DLC map Totally Insane. Remember those crazies who you dispatched with one counter and a ground takedown? Yeah, they show up here alongside lots of thugs. Except now you barely have time to do a ground takedown on any of them. Which means that they keep coming. And that's not the worst part. Said crazies can't be dispatched by any of the special takedown maneuvers and will simply leap over Batman. The worst part is that doing so will break your combo and leave you open to thugs, or even worse, more crazies.
Just before the final boss fight, Joker turns his TITAN gun on himself while talking like he'd been Driven to Suicide: "I have nothing left to live for." Fast-forward to Batman: Arkham City, and his death by TITAN poisoning.
In addition, there's Batman briefly getting infected by the TITAN formula himself near the end of Asylum, but is able to successfully overcome the effects. He wouldn't be as lucky the second time around, this time getting infected with the tainted batch of it mixed with Joker's blood, leading to far more devastating effects on his body.
The final Fission Mailed Scarecrow hallucination scene features the Joker driving the Batmobile to Arkham Asylum with Batman as his prisoner and then have him strapped onto a gunnery to be examined by the Scarecrow himself, who calls him Wayne and mocks his mental state and dead parents before letting the Joker finish him off. That nightmare becomes somewhat of a reality in Batman: Arkham Knight, where the Batman is taken prisoner and transported to the abandoned Arkham Asylum. There, he is strapped to the gunnery and the Scarecrow exposes his secret identity to the entire world and then induces him to a nightmarish fear-toxin scenario, causing the Joker in Batman's head to make his final attempt to drive Batman insane and take over his body.
Simply walking through Arkham Mansion can feel sadder after completing Knight, and knowing that Batman (well, the identity anyway) dies on the halls you currently wander.
In Arkham Knight's DLC A Matter of Family (which takes place before Asylum), audio tapes secured at Joker's amusement park hideout reveal that Dr. Young gave the park owner's terminally-ill daughter "alternative medicine", and under Jack White (Joker)'s command, gave her extra doses of it which led to her death. In other words, Dr. Young tested TITAN on a child. She may not have known that Jack White was the Joker at the time, but considering how crappy TITAN was in Asylum, an earlier version had to be even worse.
Oracle:(exasperated) What now? Riddler? Two-Face? Some kind of giant Joker robot?
When Batman talks to the Joker on a monitor early on, he quips "You were expecting Two-Face?" Not only would Two-Face appear in Arkham City, as stated above, but his voice actor in that game, Troy Baker, would go on to also voice the Joker in the prequel, Batman: Arkham Origins.
In addition, the PlayStation 3-exclusive Joker DLC has the Melee Challenge Maps in which the Clown Prince of Crime you control has lethal laughing gas, a revolver handgun, and the joy buzzer as special attacks, while he uses his impressive hand-to-hand abilities to punch, slap, kick, and poke out eyes. In Origins, you get to do the same hand-to-hand abilities as in Asylum's Melee Challenge Maps while you fight as the Joker in the Comedy Club flashback.
When Batman first meets Poison Ivy, she asks him to release her so she can help him combat the Big Bad and save her plants. Come Arkham Knight, Batman has her released from prison, works with her to fight the main villain, and he ends up saving her plants.
The final Scarecrow hallucination has your game seemingly crash before restarting. Fast forward to Arkham Knight, where the Scarecrow is the main vilain, and the game is extremely buggy, especially on PC.
A riddle that references Penguin: "A top hat and tails is the only dress code for this party in the North".
Les Yay: Harley and Ivy get their usual dose of this despite only having one (very short) scene together. Harley lets Ivy out even though she isn't on the Joker's list, and Ivy blows her a kiss as she leaves.
Joker: "I could watch those two all day. What a riot!"
The Joker teeth chattering. Also in-universe, since the Riddler challenges you to destroy as many of the annoying things as possible.
Hearing Joker repeat the same two or three lines over and over and over again as you try to Gold the challenges can get very annoying.
The raspy screams the Lunatics give off before charging you.
Some of the henchmen's lines get old quick. It can get annoying when you hear "Don't let him hit you, you idiots!" or "Get him on the ground and step on his face!" for the umpteenth time.
Game Over screens tend to become this as the game progresses, mostly due to the fact that the amount of lines the villains will throw at you is very limited (the Joker himself only seems to have six or seven of those despite being the Game Over man throughout a vast majority of the game). It doesn't help that you need to manually confirm being willing to try again rather than quit the game (despite being able to do the latter anytime you like) each time before being allowed to continue.
Narm Charm: Some of the cheesier lines come off as more than a little amusing when spoken by the always-stoic Kevin Conroy. You have to wonder how in the world Batman can keep a straight face spouting lines like "I eat punks like these for breakfast." On the other hand, it makes for a great Badass Boast.
Older Than They Think: The Predator gameplay has its roots in the Batman Begins video-game adaptation; in turn, that gameplay was based on Metal Gear Solid's stealth aspects. The heart monitor, grapple-point gargoyles, enemies becoming gradually more frantic as they're hunted, and some special attacks, all made it into Arkham Asylum.
Scrappy Mechanic: Players and critics complained that Detective Mode is just so damn handy, you'll never not want to use it, since it'll track any henchmen in the area, even in the next room, and light up secret areas - the downside is that you have to play the entire game in a blueish hue, seeing every character as a translucent skeleton. The loudest complaints came from Rocksteady's own art directors, who were upset that players weren't seeing the game as they intended it to be seen, so they Nerfed the mechanic for the sequel, making it so that certain player interface aspects were unable to be seen in detective mode.
Shipping Goggles: Thanks to the massive amounts of Foe Yay, Batman and Poison Ivy's interactions have been interpreted as them having an underlying sexual tension. Poison Ivy seems to be inviting towards Batman when she wants him to come and "see her face to face."
Poison Ivy: It's rude to keep a girl waiting, Batman.
Special Effect Failure: The Sanatorium is apparently the only place on the island experiencing a thunderstorm. This is fixed in the remastered version, which has it raining throughout the entire game.
The fight against Poison Ivy mostly has a fixed camera angle. But for a short time at the beginning of the fight, you can look around freely like you normally can. Looking to the sides reveals that the wall that was supposed to be behind you wasn't textured, allowing you to see right through to the skybox.
Squick: During the first Scarecrow segment, Joker asks Batman what his fears are, this would have been fine, but then he just had to say "Me? In a thong!?!"
Doubles as a Funny Moment, as the "Blaaaahahahaha!" that the Joker gives right after indicates that he knows that it'd be more Squick than scary, and that laugh he gives is absolutely hilarious.
During one of Batman's Scarecrow induced hallucinations there's a Batman duplicate ravenously gnawing on a dead rat.
That One Boss: Poison Ivy. It starts off easy enough, but her second phase is pure undiluted hell, especially on Hard mode. Between her fast projectiles, her constant vine waves (which seem to have a bigger hitbox than they really seem) and her hypnotized henchmen joining the fun, it's a miracle players would be able to take down her second phase on their first try. Couple that with the fact that the only real way you can hit her is with Batarangs and Explosive Gel when she goes down in that short time frame you get to hit her, and you've got one of the hardest bosses in the game.
Saving Gordon from Harley near the end of the Medical Ward. There's virtually no room for error; misalign your position even slightly, you'll immediately get spotted, which results in Gordon getting shot up and you having to start all over. Oh, and if a guard just happens to see a knocked out baddie, that also triggers the game over, so not only do you have to carefully maneuver your way through the guards, you have to make sure you take them out in very specific areas where the other guards can't find them, or you fail instantly. And after you finally manage to escape the guards, you're immediately thrown into a fight with Bane.
The Aviary in your first visit to the Botanical Gardens, for much of the same reasons as above. You can't knock out any of the guards, you can't be seen at all by any of them, and trying to get past them all with what little cover you have is pretty irritating. It thankfully gets easier once you take out the guard in the control room, but after that, there are two Titan Henchmen you have to take on at the same time.
That One Sidequest: On your way into the Visitor Center to the final boss, there's a short hallway with 20 mooks in it who won't attack you unless you attack them. You can choose to ignore them, but defeating them all earns you the "Party Pooper" achievement. Though they're unarmed, so many of them in such a tight space is extremely difficult, even with all the upgrades you have at this point.
Joker Teeth. It might have something to do with them not being an actual riddle, tape, or Arkham chronicle. Also, while about 90% of the teeth show up more or less naturally as a result of the story progression, there's that set that hide above the hallway to the warden's office, which happens after the player has realized this, and then notice they missed them after the sequence is over.