Yes it's better than DMC 4 certainly, but among the best in the industry? The biggest thing Ninja Theory added was bog standard platforming that was really held together by the visual design rather than anything gameplay wise, which to be fair is certainly better than DMC 4's Dice minigames and backtracking. However, among the best? In a world where Resident Evil 2002, Resident Evil 4, Dark Souls, Mario games in general, Half Life 1/2, Metroid Prime, 2D Metroid, Zelda, Portal, Hitman, Dead Space, Deus Ex, Thief, Metal Gear Solid, etc had already long been out? Not even close. It's a bunch of pretty hallways combined with rather standard platforming mechanics.
People tend to overrate the level design from this game a lot, its extremely linear with some parts having 2-3 paths that go to the same place very quickly nothing to write home about. The visual aesthetic is very good but the level layout is far from being impressive even if its better than the old games.
I feel like you guys are falsly equating "linearity"="bad". Not all but most of the games you listed, Crimson, have in common that they give you various degrees of freedom in how to approach (or not to approach) a situation. Certainly, all of these games have amazing level design. But almost all of them are fundamentally different to how a level for a linear character action game would be designed.
When I said it's among the best in the industry, I was saying that in the context of its genre. I think that you can absolutely make an argument that this among the, or even THE, character action game(s) with the best level design overall. The very first level is an incredibly inventive funfair, where you can throw and combo enemies into large gears after entering the backstage areas, with the gears also functioning as the a more natural version of the classic Demon Walls. The second level then gives you a lot more freedom, as you have to explore a pretty big mansion with quite a few secrets hidden away, while you at the same time keep travelling into another dimension with light platforming segments with incredible visual design. This area also functions as a tutorial, showing you that your platform skills actually allow you to manipulate the level itself, creating platforms. NT also managed to achieve the small miracle of making an actually interesting warehouse level with the warehouse exploding into a stasis full of broken shelves and platforms, which builds upon the previous tutorials as the movement here is not only more free-form, as there are various ways through the level, but it also gets combined with the combat system. A little later in the level you fight a pretty huge gauntlet of tough enemies, but the room is circular with a huge, fleshy pillar in the middle, allowing you to smartly use your platforming moves to quickly move around it, separating groups of enemies from each other and using the level to your advantage. Then comes the huge vent area where the floor changes to turn into the ceiling, back to the floor etc., introducing another element (the section is timed) to the platforming, while you also have to fight at the same time.
This is all before we even really talk about the best ideas this game had, most of all the Upside-Down-level the OP was talking about, of course. DmC constantly uses its level design to change up the combat arenas in small, inteligent ways, to give you new tools and opportunities to mix and match (and discover) your abilities, while also constantly throwing new visual concepts and ideas at you.
Meanwhile, many amazing games in the character action genre are built upon amazing combat systems that often make you walk through boring vistas and little in terms of level design that actually enhances or changes the core experience. Instead, many times, you get pretty bad mini games like the automatic "Run down this tower and evade the missiles"-part in Metal Gear Rising (which is my favorite Character Action game of all time, before someone jumps on me for "hating" on it or anything) or the whole Missile-part in Bayonetta (also: so, so, so many parts in W101).
I feel like hardcore fans often tend to ignore anything but the core combat mechanics when judging a game in the character action genre. So if I can't spend 100 hours with a combat system and still find new tricks, then that game is, pretty much by default, a failure compared to the games in the genre that do exactly that. And, certainly, the combat system is the most important part. But, as with every other genres, things like the level design is important, too. Hardcore players basically just need any old arena-styled Tower to hone their combat skills, and that's fine. But most people buying these games wil probably only play through the campaign once and if that campaign is lacking and failing to really utilize the deep mechanics of a combat system or even keeps you from enjoying them by implementing terrible box puzzle, boss gauntlets or even making you run through most of the same game again, then that is certainly worth noting and can, in combination, even turn you off of a fundamentally great combat engine.