Basically, everything you need you can get from NexusMods[www.nexusmods.com] including short instructions.
Kudos to ThunderReign [www.protondb.com].

If you'll try to play DMC HD on your Steam Deck you will immediately notice a problem - all cutscenes are flipped vertically and audio quality is... Well, bad. Since there's still no fix you can just fix it yourself, thankfully it's not hard. Your Steam Deck actually have everything you need already installed in core system (and on Linux - you can just install ffmpeg and that should be it). Although the only way you can do this is to switch to Desktop Mode. And it will also take some time, so hopefully you're patient enough. But nothing (really) hard.
... Or you can just download already modified files if you want it the easy way. Anyway, I got you covered!
Doesn't mean I can do everything for you though... So, switch to Desktop mode on your Deck and let's roll.

Easy way - I already transcoded videos for you. Download, unpack and replace original videos. As easy as it can be!
Get it from NexusMods[www.nexusmods.com]. You need to download main file.

Let's suppose you don't really trust those videos or your traffic is limited. It's fine, there is a solution too. Again, go to NexusMods[www.nexusmods.com] and download optional file containing bash script. Unpack it, go to the directory where you unpacked file, right click/L2 on an empty space inside directory and enter this command:
It will find your game on your Deck and convert all videos automatically. It takes somewhere around 40 minutes or so. After script will finish its work you can just start the game.

Maybe you don't want to download anything for some reason. It's fine too. Because it's not really hard to do it manually (althought it is a little harder and requires more steps to complete).
So, what you need to do (I assume you already switched to Desktop mode):
1. In Desktop mode open Steam, press L2 over a game in your library and select "Manage" > "Browse local files". That'll open game directory in Dolphin (default file manager in SteamOS).
2. Open the directory with video files. Easy to find since a) all videos in these directories are in wmv format and b) these directories are literally called "video". If you have trouble finding them:
2a. Launcher videos are in data/dmclauncher/video
2b. DMC1 videos are in data/dmc1/Video
2c. I don't judge you, DMC2 videos are in data/dmc2/Video
2d. DMC3 videos are in data/dmc3/Video
3. Now you need to open terminal. Easy, just move cursor over an empty space inside the directory, press L2 and select "Open Terminal Here". It'll open Konsole.
4. Paste and execute this command:
5. Now all you have to do is wait. You can go drink some tea, read a book, maybe something else - up to you. You'll see when it's done. And hear it too, Deck fans are loud.
6. It's done. Do the same thing for all other videos in data if you want - open directory with videos, open terminal, execute command.

Ok, so, explanation. For the reason no one knows developers decided to use wmv format for the videos (who in all seriousness still does that?). I mean Capcom does like to make bad decisions from time to time. Good thing is they also did a good decision to leave all videos in the open which helps us to fix all the problems. The main problem is with Proton (actually, it's that there is no native Linux port but we'll skip that) - it doesn't handle wmv files very well, so we have flipped videos. Audio codec, while works, also isn't exactly great and Proton implementations isn't great either. Basically everything is a recipe for a lot of problems.
But what exactly we did by executing script (or command, if you like it the hard way)? Well, we looked at each video file, made a copy with mp4 video codec, with vertically flipped image and with audio with a better codec, then we removed the original video and replaced it with copy. Yep, that's it.
You might have a question - how does that work when codecs are different from what they should be? It just shouldn't work. Well, I believe someone just didn't give a damn and decided to skip the check. As of an embedded video player that is used - it does seem to actually support mp4 codec. Which also brings the question why wmv videos were chosen in the first place.
Anyway that should be it. Boot the game and go kick some demon's ass.