I just want to add some input from my experience with level design in general. I'm not a professional level designer, I'm just someone that makes levels with tools that I find on the Internet out of a passion for platform and 2D games. I feel a lot of levels fall by the wayside for a few reasons and if you've not grown up practicing level design, they can be easy mistakes to make.
1) Firstly, graphics and atmosphere. The internal graphics of vvvvvv don't have a huge amount of assets, but still, an endless amount of good looking screens are possible. When carving out caverns, even if the shape is arbitrary because it's just a linker screen, there's a certain feng-shui that can make even a dull, challengeless corridor pleasing to navigate through. Think about tiling and avoid tiling issues by using direct mode. Try and give your environments a little bit of history, like some paths which look like they were once passages but have since caved in, structures which would have been symmetrical but have eroded away. Use stuck spites or coloured blocks to make features like machinery, water, fog, etc... A good balance between symmetry and asymmetry is a handy thing to learn, because screens that are mostly symmetrical but with a few breaks in the symmetry tend to be memorable to the mind.
Atmosphere comes from making your level feel like an adventure, a series of locations that flow onto eachother rather than a bunch of screens strung together (you might notice, most of the Featured Levels have done this to some extent). Add some stuff that doesn't benefit the gameplay, but gets the imagination working. Think environmental... Then you can create something that is more than just a video game level, but something that suggests an actual place you're exploring, which just happens to have game-like challenges in it. A classic trick in flickscreen platformer design is to tuck a passageway out of the way, running through a few screens where you can't get to it. This is called a "promised land" and subconsciously gets the player really wondering how and when they'll be able to get there. Avoid giant rectangles that break up the screen in an awkward way, and other ugly things. Just look at the level design for the original vvvvvv - the layouts just invite the eye and the player's avatar to explore them.
2) Difficulty. I don't mean to bang on about my own work, but I learned a lot when I had to make the easy mode version of d.333333. Because the original version, while reasonably possible to me and a few other expert twitch platformers, was just putting up barriers to most players. When I made the entire level easier I stripped out enemies, I made windows of opportunity wider, I added parts of walls that were spikeless, so the player could brush against them and use them to help get aligned for tougher moves in mid flight. I believe I managed to take pretty much every puzzle and make it more fun for the average person, while still retaining the core essence of what each obstacle and puzzle was imparting on the player. THAT is your job as a level designer. So I learned something important: There is fun difficulty and not so fun difficulty. The prototypical example of unfun difficulty is trying to line up into a 2-block hole in spikes in freefall whilst dodging an enemy. Sure, if you achieve it, you might feel good because you showed skill. Or you might just feel you were brute forcing the solution until the Timing Gods allowed you to pass via a random dose of good luck. You want the player to have to think about what they need to do, but not feel like they should rely on luck and endless repetition to finally get it down.
3) Tiling errors. Ok, some levels are uniformly scruffy/glitchy and have a kinda cool look to them, but if you're going for something immersive, NO FLOATING SPIKES unless you can make it look like they're stuck to a background panel. No platforms with only half of the outline intact. Direct mode is a thing now, you have total freedom to make spikes and wall borders look good, make creative joinery work between walls, creative flourishes, etc.
To be honest I see a lot of levels breaking these rules and there are plenty of good levels that could be great levels with a bit more care and attention.