Every time I disassociate from my human body, an announcement is made in chat that I've again made the advancement [A devilish conundrum].

Does this happen without other mods ? Which version are you using ?

I tested with only Requiem 1.18.1 beta 5. No other mods were used.

Same

Are you somehow revoking the advancement anywhere at any time? If so, that may be what's causing this issue.

Or it could be that the shell Player is spawned without the original Player's advancements, and the shell is awarded the advancement when the Player disassociates from it.

This has been fixed, shells do not broadcast advancements as of a few beta versions ago.