Yes an no, I don't understand how all the challenges are stored, however under the 'raw tab', some data is stored in LevelChallengeUnlocks and OneOffLevelChallengeData.
Do play around with them if you are interested, I have a thread with profiles all having completed challenges here that I done using the editor. Those two parameters trigger particular challenges. I believe LevelChallengeUnlocks may tie specifically to the level challenges like Cult The Vault, they trigger an entry once completed.
I have been thinking as posting this that OneOffLevelChallengeData may refer to the turret challenge that you only have 1 opportunity with @ Eridium Blight. However I don't think that's the case, more testing would be needed. EDIT: Another option would be the weapon slot upgrades, will test later.
There are a few things I do know, challenge data is tied to the save. Weapon, shield etc. challenges cannot be converted to PC via. an editor save; however all level challenge data will, all challenges remain complete between class changes using the same save file. The non-level data gets reset I presume as they are stored differently.