I wouldn't call this a campaign either. If there was a story, then maybe.

I've always wanted a Toribash Story Mode (hence the Video Series I made on Youtube). Similar to this idea but there is a narrative and characters for the player to progress through.

But without the narrative or story, but just challenges and levels. It'd just be a revamped tutorial, as McFarbo has stated.
or a "Toribash Challenge Mode".

But if you want Ideas for a story mode, i'd say you could do cut scenes in the way that Jisse keyframed his John Wick replay so you can have jump cuts and camera pans and movements. Each Cutscene can be like a replay. And when you play story mode or download it, or however it will come, it'll be a large list of replay cutscenes. And you have to do something to unlock or gain access to the next replay, (scene/part of story) And use the dialogue in the Toribash Tutorials the pop up when you do something or just the general text area, to insert dialogue. Maybe even Responses to questions could be similar to typing in commands. But that'd make it a little more complicated.

I'm not quite sure how easy or hard any of that would be, it's just a theory.

You can have mods made for different scenes/levels. And Textures made, for characters in the story mode.
if you need story ideas or someone on the team to create/organize/map stories, it's basically what I've been doing for the past 4 years on this game. So just let me know.

If you're worried about choosing too much tutorial or too much story mode, just include the tutorial at the beginning of the Story Mode or plant them throughout.