Back in the day I used to use "The Backloggery". Although I still think that The Completionator is much better and has a lot more features, one of the features I miss most is the, "Mastery" status that The Backloggery has.

This was a gameplay status that was even higher the "completed" where you would be required to do a personal challenge in the game. For instance, "beat the game without dying", "beat the game without jumping", "beat the game without a sword", etc.

I'm not saying that is has to be a full on status but I think it would be cool if there was some way to track these things.

Currently, I have just been putting my personal challenges in the completion notes, but I think it would be nice to be able to sort by them and see them all in one place.

What do you guys think?

Sounds like you handle them the same way I do, with completion notes. It's "fine" but definitely suffers from not being able to be filtered if you want an overview of your challenges. I mean, Speed Runs are basically a type of challenge run already, but a mechanic to track any kind of non-standard way of playing would be nice.
If a tagging system (like the one from the collection page) were added so you could have something to filter by, that would probably work rather than adding a number of different status types.
Conversely, you could also say, change out "Speed Run" to "Challenge Run" with a sub-menu of challenge types if it were to be curated (good luck creating that list with all the variants of challenges out there though.)

Challenge Run:

• Speed Run
• No Death
• No Damage
• Solo Run
• Blindfolded
• etc...

I like the idea of having a Challenge Run completion type. I agree it would be tough to have a complete list of "possible" challenges since it's essentially infinite. But if we have the most common, plus the existing notes field, it seems like that could cover the vast majority of cases.