So anyway, I'm interested what other people who've played through the game on Ace and Insane will think of this analysis. Or whether I'm completely wrong!
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This is all also based around consecutive playthrough, not cold-starts. I don't think going the other way would change very much about this, but it might affect some of the specific examples.
Zeta Aquilae
The difficulty here is built around having to dodge large numbers of very different types of projectiles at the same time. As the system goes on, the number of enemies you face at one time increases, and the space you have to dodge starts to get a little tighter and more vertical. It culminates by introducing you to flash missiles and homing missiles, and then pitting you against a boss which uses both.
Quartzon
Extremely interconnected spaces with powerful roaming enemies that force you to watch your back. The water environment is designed to play into this, with waterfalls that aren't damaging but are loud, making it hard to detect enemies approaching you from places where you aren't looking. As it goes on you start to get ambushed by more dangerous enemies, while level traps and mine laying bots make strategic retreat more difficult. It culminates in a level where most of the interconnections are vertical instead of horizontal, and a boss that uses a low-visibility arena to lay mines and launch sneak attacks.
Brimspark
Medium to large spaces with enemies that force you to stay away from the walls. As it goes on the spaces get larger, homing missiles and swarm attacks become more frequent, and enemies start to use lava falls as strategic barriers that make them difficult to approach. It culminates with some of the largest spaces in the game and a boss whose mega missiles have a huge blast radius. The whole thing is kind of a warm up for Puuma Sphere.
Limefrost Spiral
Medium to tight spaces with a lot of verticality, many roaming and other powerful enemies, all of which often attack from above. As it goes on the levels get more and more vertical, and the roaming enemies get more powerful (though the others stay about the same), culminating in a level with some of the most vertical spaces in the game and a boss that can blind you and open you up to attack from all sides. Also the first part of the game where energy gets hard to find -- energy centers, when they exist at all, are fairly deep into the level and often in hard-to-reach places.
Baloris Prime
The hardest one to nail down, and one of the most interesting
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This is also, as far as I remember, the only point in the game where thief will usually show up at the end of the level, instead of the beginning. This gives you the option to ignore him and just go for the finish, but comes with the risk where if you do that he might take something vital from you during the countdown when you can't get it back.
And Baloris is also, if you just count by the sheer number of individually-dangerous bots attacking at once, where you get the biggest fights in the game. So it's got more stuff going on, but that stuff is still consistent.
Puuma Sphere
Very tight spaces with enemies that force you away from the walls. Any energy is very awkwardly placed, and very heavily guarded, when it exists at all. It doesn't change much as you go from 21 to 24, except for already-frequent homing missile attacks becoming even moreso, swarm attacks becoming more dangerous, and the amount of available energy fluctuating wildly up and down. Basically it's Brimspark 2.0, with less energy.
The final boss, though, doesn't really relate to the rest of the system in the same way the other five do.
Vertigo Series, again as far as I remember, uses some of these challenge "archetypes" sometimes, but doesn't progress them in the same way, and is just as likely to take a more D1ish difficulty style, mix several together, or invent an entirely new one. So if I were to go into Vertigo I'd have to take it level-by-level, and I'd want a chance to replay it first.
From memory, though, the one really big difference Vertigo seemed to have is that energy scarcity doesn't really enter into the equation outside of a few very specific situations.