Blah I typed up a long version and accidently hit back, lost it all.
I'll retype it, but not as detailed:
Tank Party: PLD/NINx2, BRD, WHM WHM RDM
Melees: 2 SAMs are sufficient, or DD subbing SAM
Mages: 3-4 BLMs, RDM (MP wasn't a big issue)
When you pop it, it will be at 50% HP with one head, wait 5 odd minutes for it to Regen to 100% (and 3 heads) before attempting to hurt it.
Tinnin's pattern of attacks:
Melee -> Polar/Pyric Bulwark [Gains Magical/Physical Shield respectively] -> Immediately performs an AoE Curse+Poison move (tanks need to be cursna'd and poisona'd immediately here) -> momentarily "stunned" -> melee
It cannot be kited. It draws in. Take care to NOT trigger draw in, each time it does it will perform a special move outside of the pattern above which will cause unexpected damage/curing. Also, if someone does get hate and Tinnin turns, respostion immediately or it'll use a Spike Flail type move called "Serpentine Tail" which is a single target move doing 2000+ damage. Hate needs to be managed good. Tanks should Cure IV themselves after they are uncursed for hate.
If you trigger draw in it will either use: Barofield, Trembling or Serpentine Tail (depending on what happens).
Tinnin can be Slow2 and Elegy'd, making tanking quite simple. Best to have a primary tank tanking with the 2nd on curing duty incase the first tank goes down. But if you don't trigger draw in much one tank is quite sufficient. Backup is always nice.
Otherwise, 2 DDs should try to Trick Attack onto the tanks and perform a skillchain for the BLMs to burst off from as the main source of damage. If all goes well the battle should only take around 1 hour.