After spending more time with the demo and trying to min/max kill time, I can say that I'm looking forward to this game even more.
After looking at your video, I did a few things differently that I think helped.
I know you were aiming for no damage, but at the very beginning of the fight and when the scorpion jumps back down in the 2nd phase, I like to use the parry from punisher stance.
During the first phase, you can make the scorpion fall down and put it into pressure just by doing a punisher combo berserk buff then two more punisher combos. Don't even need to use the fire. Then, I use those two ATB bars to do punisher combo -> cancel into Focused Thrust -> punisher combo -> cancel into Focus Thrust to stagger. Since Barret still has the ATB bar, I can use that to thunder with 1.6 damage.
Then,, at the start of phase 2, I have already built up 2 or almost 2 ATB bars with Cloud. Instead of two fires to hit the field generator, I go to the rear of the scorpion do a half punisher combo into berserk buff, then fire to kill the shield. When the Scorpion jumps on the wall, I shoot a fire with Cloud and a Focused Shot with Barret. Scorpion jumps back down, parry/counter with Cloud into more punisher combos to make the Scorpion fall, Punisher combo -> beserk buff -> Focused Thrust to stagger, then another thunder with Barret.
At the start of phase 3, Cloud should have at least one ATB bar and the berserk buff still active, so I have him throw one fire while he's running to the debris.