Here are some videos of "interesting" solos if the OP is interested in player-made challenges. Including a solo of that Lv99 Qiqirn Mercenary someone mentioned. Solos were done by either myself or another player on my server Roi Beoulve.
Lv99 Qiqirn Mercenary by Lv50 GLA
Lv75 Widowmaker by Lv50 GLA
Lv70 Ogre by Lv50 GLA
Lv91 Rainbow Basilisk by Lv50 ARC
Uraeus by Lv50 THM
Great Buffalo by Lv50 THM
Elder Mosshorn by Lv50 THM
Dodore (Un-nerfed Version) by Lv50 THM
Haughtpox Bloatbilly (Un-nerfed version) by Lv50 THM
Tarbh Uisge by Lv50 THM
There are many aspects of the current XIV battle system which are "broken" and make these solos possible (some of them with relative ease). Just to list a few of the really big ones:
(1) Aegis Boon and Deflection being broken (Aegis Boon at least a glitch)
(2) dLVL-ignoring attacks (Bloodletter, DoTs, Barbs) being very strong on high level mobs
(3) The "return to territory" mechanic being extremely abusable
To add a couple which I'm sure you've seen from these group kills:
(4) The fact cures generate almost/no enmity.
(5) Twisting Vice being extremely overpowered as a TP-control strategy
Hopefully many of these mechanics will be changed (in as little as a week from now). I think it's fun to challenge yourself or you group, but as others have mentioned, there is little reward for exceling beyond maybe farming the NMs solo/low man for selling right now. And with all due respect to the players that posted the Lv87 Ogre video in the thread that got locked, there is no mob challenge that truly requires anything beyond 2, maybe 3 players in this game currently, although that shouldn't diminish their own sense of accomplishment.