Black Mages have solo'ed several things, from sea mobs to ENMs to KS30s to Apollyon NW.
Well, I've stumbled across this video that presents something new for BLMs to try and solo- Waking Dreams, better known as "the Diabolos fight."
Enjoy!
Just in case the above video does not work, you can see the video here, along with the rest of Vol's solo feats (including Ark Angel MR!)