Hey all,
This is a copy of my guide that was originally posted on Reddit. I have removed it and linked to this post for future googlers.
The first thing you will need is SteamTinkerLaunch, installation instructions can be found here. Be sure to check out the "distro specific instructions" section.
Now add SteamTinkerLaunch as a compatibility tool, instructions to do so can be found here.
Next, in your Steam library, right click on Spelunky 2, click Properties, check the box next to "Force the use of a specific Steam Play compatability tool" and select SteamTinkerLaunch.
The next thing you'll need is Modlunky2, which can be found here. Just download modlunky2.exe, and place it in Spelunky 2's directory. You can find the directory by right clicking the game in your Steam library, hovering over Manage, and clicking Browse local files.
While you're here, it's a good time to backup your save file if you care about your progress. Just copy savegame.sav to somewhere safe.
Now Launch Spelunky 2 from Steam. A SteamTinkerLaunch window will pop up, click Main Menu when it does. In the main menu, click on Game Menu. Near the top of the game menu, check the box next to Use custom command. To the right of Custom command, change Spel2.exe to modlunky2.exe.
Now scroll about half way down the game menu until you see Proton options, and change the Proton version to Proton experimental.
Finally, click Save and Play. Modlunky 2 should open and you can begin installing mods!
The process of using Modlunky 2 and spelunky.fyi to get and install mods is identical to Windows from here on out, so if you need more guidance you can follow any of the existing guides for doing so.