In order to unleash dark phoenix, you have to make sure that before she dies, you have five full hyper combo bars (that bar in the corner of the screen). So when you play phoenix on your team, don't waste any of those bars, save em up. Also, it'd be good to save x-factor for dark phoenix since she's so deadly with it.
I was hoping to come up with a question while objecting. I didnt. -Miles Edgeworth.