Anti-Climax Boss: Despite being Dracula's son and one of your partner characters, Alucard's boss battle is a joke, and any decent player will be able to beat him with just the Whip without getting hit. In short, when he appears to attack, you can simply just jump and whip his head, then whip his fireballs as soon as he fires them, destroying them all and easily blocking his method of attack. Then when he transforms into bats to move around the field, they move so slowly and give you an eternity to make sure you get out of the way before he reappears to avoid Collision Damage. He is even easier in the Famicom version, where he only deals a measly 2 bars of damage instead of 3, and his fireballs are significantly slower if you for some reason actually let him fire them.
Breather Boss: In the Famicom version, the Bone Dragon King, as his entire body can be attacked to harm him, which has a twofold effect; it obviously makes him a lot easier to hit, but due to each of his segments having individual hurtboxes, it also allows single attacks to register multiple hits on him. So even though you fight him in an area where you risk getting knocked into Bottomless Pits, you can deplete his lifebar ridiculously fast and end the fight before it even really gets going. Then when he reappears at the end of the second part of the level, he'll have almost no health left and can only take 2 more whip hits, making the rising water a nonfactor. This isn't so in the NES version, however; there only his head can be harmed, making him a lot more difficult to hit and removing the ability to register multiple hits on him with a single attack, and he leaves the first fight sooner, so when he reappears for the second fight, he'll have nearly half his health for it, which, when combined with the difficulty of hitting him, makes for a true Time-Limit Boss.
Also in the Famicom version, the Spirit at the end of the Pirate Ship and both Stage 7s. The Famicom version gives you spots you're completely safe from the Mummies and Cyclops while you're still able to hit them, killing them effortlessly and leaving just the Leviathan as the only threat to deal with, which even with him killing you in four hits at full health, should be killed without much trouble with all the health you'll have from cheesing the two prior battles. The NES version adjusts the Mummies so their bandages fly in a wavy pattern that will hit you in these safe spots and can't be avoided by just ducking and whipping in place, while the Cyclops can now walk under the platforms and thus no longer making them safe to camp on, and the Leviathan also got a buff in its fireball attack being revamped so it's much more difficult to avoid, overall making the Spirit in the NES version considerably more difficut and no longer a breather.
The Cyclops at the end of Stage 3 on Sypha's path. You don't ever need to get off the platform you start on where he can't reach you, so you can just go on the platform one step down to duck and whip his head when he approaches, jump back to the starting platform when he's too close, and go back to the step down when he walks away, repeating until he dies without ever putting yourself in danger of ever getting hit. This breather is especially apparent if you opted to do the Clock Tower before Stage 3 and fought Possessed Grant, a considerably more challenging boss.
Breather Level: On the Alucard path, opting to finish Stage 5 rather than going to the Sunken Ruins, takes you to the Catacombs beneath the castle for Stage 6. It's unusually short, has fairly simple challenges, and both Grant and Alucard have ways to make it even shorter. Even the boss (Frankie, who appears in Stage 5 of Sypha's route) is pretty easy.
The Castle Entrance is this on all paths, despite the fact that from this point on you die in four hits. It's short, light on the bottomless pits and tricky jumps, and allows opportunities to get lots of hearts. The boss is certainly not easy though, considering it's Death.
Demonic Spiders: On the hard mode of the NES version, the Skull Heads that replace the Medusa Heads. They're far worse than the Medusa Heads and Bats, flying in an incredibly erratic and unpredictable pattern, while they're capable of flying up or down the complete screen worth. They'll additionally always deal 4 bars of damage when they hit, and some level screens that didn't have the Medusa Heads have the Skull Heads flying around on the hard mode. On screens they appear it's pretty much RNG if you'll make it through without getting hit, and unless you have a Stopwatch with enough hearts to spam it until you make it past them, you're nigh-guaranteed to take a hit or two from them and lose a lot of your health in the process.
Ensemble Darkhorse: Alucard was a relatively minor character in this game, but he evidently had enough of a fanbase to later become the main character of Symphony of the Night. After Alucard's breakout into one of the series' more popular characters, usually Sypha takes the spot, since she's less than likely to return in games that didn't cover Dracula's Curse (needing to have other mages, preferably her descendants to represent her), but she remains popular as the mother of Belmont's magical gene (and tends to be portrayed without her hood afterwards, making her more blatantly attractive from get-go) and being a Game-Breaker that will definitely help the game's difficulty.
Game-Breaker: Sypha's Lightning spell; it shoots out three large blue orbs that fly around the screen, each individually dealing twice as much damage as Trevor's full-powered whip, and they go through targets and can individually strike multiple times as a result. It'll lay waste to any normal enemy, while trivialising most bosses in the game, and it only costs a single heart to use for each use. You can't get the double or triple shot powerup with it, but then it has this game-breaking power upon immediately obtaining it. The only real downsides to it are that it's the rarest subweapon to find in the game, and you may find one orb not homing in properly and circling around its target without hitting it and not leaving the screen, where you're then unable to fire out another Lightning until it finally goes away; this is particularly prone to happening against Dracula's final form.
While Holy Water no longer completely stunlock bosses like in the first Castlevania, they still barely move while being burned by it and a triple shot Holy Water will utterly destroy bosses in a few seconds just like in the original game. There are a few more bosses in this game that fly or require their head being struck to harm, so triple shot Holy Water isn't an instant win all the time, and the significantly more difficult levels with vertical platforming will make carrying Holy Water around as your subweapon not always ideal. Regardless, triple shot Holy Water is still a game breaker against a good amount of bosses, including Death, the Doppleganger, and the Skull Knight King, the hardest bosses in the game outside Dracula.
Good Bad Bug: When fighting the Doppleganger, when you switch characters, the Doppleganger will transform alongside you. However, it doesn't transform during the switching process, instead taking a second to transform after you switch, where it is completely vulnerable. A player can exploit this by switching, taking a shot at it, then switching before it can attack or move, and repeating the process until it dies without ever getting a chance to actually fight back.
Scrappy Mechanic: The stairs. Stairs severely limit your mobility, and due to pressing up at the base of stairs or down at the top of them causing you to go on them, you will inadvertently find yourself going on the stairs when trying to crouch or use a subweapon near them, often causing you to needlessly take a hit. The control conflict with subweapons also means you can't properly use subweapons on stairs, as many of your subweapon inputs will not go through, which, when combined with the aforementioned mobility issues, often leaves you a sitting duck on stairs. While these problems were in the original Castlevania, stairs are a lot more prevalent in this game, and there are many vertical platforming sections that requires you to go on stairs unlike in the original game. Then there's the fact that one of the playable characters, Alucard, inexplicably can't use his basic attack when on the stairs, leaving him completely defenseless on stairs.
The Doppleganger, who'll give you quite some trouble unless you exploit the aforementioned glitch to defeat it, especially in the NES version where it deals 4 bars of damage (in the Famicom version it deals 3 bars of damage instead, giving you a bit more leniency against it). If you're playing a Trevor solo playthrough and thus won't have access to the aforementioned exploit, you better hope you get to it with Holy Water intact.
Death is this as usual. He flies around summoning scythes and you die in four hits like the encounter in the first game, only he has a second form this time round. Fortunately, the second form is easier than the first form, and the first, while really hard, is not as brutal as he was in the first game. This is due to you having more options and room to maneuver in the room you fight him, Death's first form having a lot less health (requiring 11 whip hits to defeat here compared to 16 in the original), and unlike in the original where you had to go through a notoriously difficult hallway full of Medusa Heads and Axe Armors to get a chance at Death each time, Death's hallway has nothing but a collapsing bridge and a lone knight, while it gives you your choice of any subweapon (alongside a free double shot for a Cross).
The Skull Knight King who appears at the end of Stage 5 if you continue along the Catacombs in Alucard's path. He's exactly the same as the Warmup Boss from the first level, except this time whenever you hit him, a bone projectile breaks off that circles around him and homes in on you, while never disappearing unless you hit them. These bones are extremely hard to hit, and are about impossible to avoid for long, especially if there's many of them out at once, while the Skull Knight King relentlessly pursues you. Additionally, if you end up on the left of him, there's no platforms to jump up on and only a long flight of stairs, so your only way to avoid getting hit by him here is to climb up the stairs, which leaves you a sitting duck to his bones. Also the Skull Knight King has increased health and requires 16 full-powered whip hits to defeat, meaning that's a minimum of 15 bones you'll have to deal with. Then for the kicker; if you die at any point on this level, the only subweapon available in the entire level is the Knife, which is mostly useless against him. So you'll essentially have to beat him with just your whip, if you don't carry a better subweapon from a prior level without dying here. The saving grace against him if you're stuck here without a good subweapon is that when he's attacked with your whip, he'll attempt to shield your attack and then counterattack with his sword that your full-powered whip outreaches, so if you can get him at the right spacing, you can keep whipping at him over and over while he's stuck in the same spot, damaging him while simultaneously destroying his bones as they're released until he dies.
Stage 7-5 on Alucard's path. The only way to advance was to wait for the falling blocks to form a platform for you to ascend. If you got hit by a falling block, you were likely dead, and had to repeat the process from the start. If you brought Alucard along and had enough hearts you could just fly up and skip this part entirely, though if you brought Grant or went solo, you're SOL.
Stage 7 on Alucard's path as a whole could count, seeing as it's about as long as 2 normal stages. The best part? The hardest parts are AFTER the falling blocks, so every time you game over, you have to go through them again. It also has a fairly difficult Sequential Boss at the end in the NES version, where you had to fight a pair of bossified mummies, a Cyclops, and the Leviathan, a Damage-Sponge Boss who had over twice as much HP as most other bosses and marks the point in the NES version where enemies start dealing 4 bars of damage, while being one of the few enemies in the game to deal 4 bars of damage in the Famicon version (on the Famicom version you get a bit of mercy though against this trio as covered in the Breather Boss section).
There's also Stage 9, which is almost all the different challenging segments remixed into one big ass and really difficult stage. The fact that you die in four hits at this point on the NES version is the icing on the cake. And it ends with the aforementioned Doppleganger fight, a really difficult boss fight if you don't use the aforementioned exploit to beat it or don't make it to the fight with Holy Water intact.
Block 6-5 of the Sunken City, when on the hard mode. This is the section after the Bone Dragon King flees from its first battle, where you have to escape a rising flood and finish off the Bone Dragon King before you're overtaken by the flood. This section is pretty difficult in the normal game, but in the hard mode, the flood rises twice as fast, and there are Bats EVERYWHERE; you can have as much as three Bats on the screen at once, while still having to contend with the Mermen jumping out of the water and most of the blocks breaking away if you stand on them for too long. You're going to get hit by suddenly spawning Bats a lot, often being knocked into the water for an instant death, or get trapped in a spot where you need to take a hit or die. And of course it's even worse in the NES version, where everything will be dealing 4 bars of damage to you, so you are just as likely to die from getting hit just 4 times as you are to die from being knocked into the water, while the Bone Dragon King's extra health in the second battle is a much bigger deal when the water is rising so rapidly. Having Alucard to skip over most of the platforming is a lifesaver, otherwise you're going to need the Stopwatch to not depend so heavily on RNG to get past the constant Bats, in which case you're going to have to fight the Bone Dragon King in both battles with just the whip if you want to use the Stopwatch for this section.
Viewer Gender Confusion: This was especially common with Sypha before the days of the internet. The only way you found out she's a girl is beating the game with her as your partner. Considering how difficult the US version is, that's no small feat for kids of the day. The fact that the text leaves the prompt as "Take him with you?" on her select screen doesn't help. In Japanese, it was perfectly fine using gender-neutral pronouns.