Cuphead is a 2D side-scrolling shooter/platformer hybrid. Its reputation for being hard is deserved, even without the unfair aspects. I quite like the game. The unfair aspects can be mitigated with the wiki and youtube (and there's no major spoiler potential to worry about), and overall the game is great.
Cuphead has an equipment system, but shows no quantitative information, you can't sell anything, and the system itself is not well explained: the description of charms makes them sound like passive upgrades, not equippables, so I initially bought two charms without realizing you can only equip one at a time.
The wiki's list of shots is highly recommended reading before buying anything.
Trial and error
There are a lot of enemy patterns that require foreknowledge to avoid, objects that look dangerous but aren't, objects that don't look dangerous but are, etc. I can list a ton of offending examples off the top of my head:
Rumor Honeybottom's saw moves way too fast to react, and see how subtle the telegraph is? Even if there were nothing else on the screen, it doesn't even look like a telegraph. It just looks like a normal movement animation.
Captain Brineybeard's boat's laser is the same way: zero time to react, and the telegraph doesn't look like one.
In the beginning of Djimmi the Great's last phase, his hands are not dangerous, but they look like they are, and thinking they are makes it almost impossible to avoid the pyramids.
Or this miniboss's shockwaves when he jumps. Would you even guess it's a shockwave? Those little splashes look cosmetic, but they're dangerous, and good luck guessing exactly where the boundaries are.
Or check out this squid. Pink things can be jumped off, but not when they're not pink, so before I jump on it, I can only assume I'm supposed to jump off that gem to avoid contacting the enemy and then land on something else out of view. I was shocked to find there's nothing on the other side so I fell in the water and died. As is typical for the genre, most enemies damage you on contact, so imagine expecting the player to know that you're actually supposed to just stand on the squid's head!
Oh, and could you guess that when the squid's gem turns pink again in a few seconds, you have to hit it again or else the squid sinks? I couldn't.
It seems to get worse later in the game. I don't remember it being that bad in world 1, but in world 3, every level has two things like this.
There are a few hilariously underpowered items, a few reasonably underpowered ones, but there aren't any overpowered ones. There are a few different weapons and a few different charms worth using in different levels. A lot of depth also comes from the ability to switch between two weapons inside of a level.
Cuphead inherits a flaw common in arcade-style shooters, which is that you almost always want to be shooting, which means you pretty much hold down that button the entire time you're playing. It makes my finger sore. Solving this problem in Cuphead isn't as simple as "just make the player constantly shoot" though, because there are some situations where you don't want to shoot, they're just few and far between. I'd like to experiment with a button that suppresses shooting instead of a button that shoots.
Sectioning and saving
Cuphead does all of this right: it saves automatically outside of battle, there are no in-level checkpoints or consumable items to speak of, and no status is preserved between levels. You can also replay old levels (to get more coins if you missed some of them before, but not to re-collect the same coins).
Most levels are about 2 minutes long and retries are quick. The only change I'd have made is more health. 3 hits for 2 minutes is low enough that being hit can be very tilting. I'd have it balanced for 6 hits per level.
It has a weird deal with the easy mode: there is one, but from what I'm reading it makes your wins not actually count, making it basically pointless (soul contracts are required to proceed so at most you could play all of world 1 this way).
There is an unlockable hard mode. It sucks that it's unlockable, but at least the normal mode is hard enough that no one would need it on their first playthrough.