Here's how it went:
[spoiler]Well I think it took between 20 and 30 turns, I feel like I kinda cheated because reading this boards I inevitably found out about Aegis defense and I had it before the fight, so it was a matter of guessing the activation, not so hard. Also I waited a couple turns for the final blow since I read that he blew up when disjointed
Anyway, I discovered after the middle of the fight that barring my arbalist critting for more than 500 damage with normal attacks (night vision), the most effective character was my buccaneer with a single point in chase ice (everybody else had icy weapons), which seems to retain the elemental properties of the weapon for massive damage (he had the gun with three preset flame slots), each chase did something like 130 damage, 250 critting, while rapid fire in comparison did not much (three shots for way less than 100 damage each)... Not sure about the actual pure damage since buffs were coming and going but still the impression was that the chases hit a lot harder.
The Ninja cloned himself whenever possible and then just attacked (50 dmg x2 :\... just took the zodiac subclass, not much to do right now in boss fights), the Princess buffed the buffable (plus some very light healing, items, and rare attacks when needed), the Hoplite covered her ass and everyone else, the Buccaneer shot like crazy and Eagle eyed the boss whenever possible, plus it seems to me that I was able to Aegis each beam attack only because of his maxed limit boost, the other two had always a couple of pixels in the bar left prior to the attack... the other tactic i used was the Charge one.
Noone died and I used three amritas and a couple of madora during critic moments (notably when the head was disjointed from the body)... it was not a piece of cake but it could have gone a lot worse, I guess.[/spoiler]
Just took a couple of steps into the 4th stratum and it really seems something else!

