I think I recall you have Status Reels. So what I'm thinking is to Haste Wakka and Terra, have Wakka open with Status Reels to the head, and then Thundaja the head. If I recall the head has about 25k HP, so a Status Reels followed by a Thundaja and it should need only 1 or 2 more attacks.
I couldn't be 100% sure if it was the head or the body using Thundaga. If it's the body then killing the head might not be worthwhile because it won't do anything to stop the Thundagas.
Once the head dies if you leave the arms alive it doesn't really do a whole lot of physical damage, so you could just fight through the high defense with Armor Break and magic spells.
The body only ever casts Graviga and uses physical attacks. With Protectga up, the physical attacks are mostly harmless, even if both arms have been destroyed.
It's definitely the head casting Thundara, because I just had an insanely lucky run where Thundara was only cast once and otherwise the head spent every turn "moving suspiciously." With Wakka spamming Armor Break, Double Cut, and Status Reels, the "moving suspiciously" turns bought me enough time to kill the head.
Afterward, my abilities were bone dry except for some double cuts on Locke and Retaliate on Cloud (which was 100% useless for me because Cloud does less damage than Tidus or Wakka, and about the same damage as Locke.) I could post my setup, but I don't really think it should be used as a model. I lucked out big time.
I do still think that burning down the head as fast as possible is the way to go. You mentioned Status Reels + Thundaja and I bet that would be a good approach. With Boost, Wakka was hitting for about ~2500 I think. I brought Locke + Mirage Dive as my RW--his attack damages the head, but nothing gets slowed. Tidus' Spiral Cut only hits the body and arms, though.
And with that I've mastered everything in the Tidus event, so I guess I'm waiting until the Bonus Battle gets added. Valefor hype!