I've heard of BST's duoing Hakutakku. I could see a BST potentially soloing Hakutakku as well. Any other job I'd be skeptical of soloing it.
The combination of AM, -ga spells, a nasty paralyze (Hex Eye), strong resistance to debuffs (anyone but a RDM generally has their debuffs wear in a few seconds, if they stick at all), damage that bypasses shadows (Death Ray, Blaze Spikes) and hard hitting melee attacks (400-500 damage per hit to a LV 75 melee with Berserk up is fresh in my mind from our last run), all make it very hard for a single player to fight it. Plus, Hakutakku can't be kited because there is no place to run him for very long. Even if you kill all the Million Eyes in the area before the pop, they will respawn long before a "DoT and Kite" strategy would kill him.
To counteract all of Hakutakku's abilities, in addition to heavy and continuous damage dealing capabilities you would need:
A. Stun, Dispel, Shadows (or one hell of a VIT and DEF rating with maybe some damage reduction), HP recovery of some sort and Paralyna
or
B. Cannon Fodder, ie pets
or
C. Hacks
Now, some of the assets in section "A" could be covered by meds, but it would be very expensive and take lots of inventory space. Also, NIN/DRK could face away and just spam the elemental wheel, casting Stun when needed... but the fight would be so long that the chances of an uncontrollable disaster occurring (such as back to back -ga spells followed by several of Hakutakku's melee attacks hitting before shadows can be reapplied) reaches a near certainty.