How to do this achievement?
No matter how much I exhaust her, the achievement does not count.

it's the hidden stagger when he's in phoenix mode (before fleeing).
Purposely fail the bar stagger twice in row so he turns into phoenix mode.
Wait more and he'll roar, it's an hidden stagger (no bar shown), if you succeed it, you prog the achievement, if you fail it, he flees and you need to flare/phero.
After that, he goes back to normal mode, and you can redo the same, with a properly underequiped char you should be able to do it 2 or 3 times before he dies.