O Ilusionista,,
I took most of my design inspiration from X-Men Evolution and the movies. Yeah, I know they have their detractors, but I really like the way Kitty was portrayed in them. As part of that, no dragon. The dragon thing to me is an albatross. A very stupid addition that adds an unnecessary element to what should be (or was) a kind of down to earth character. Take of that what you will, your designs tend to be much closer to the comics, so you might think very differently.
Anyway, on to making it work...
The idea for my own project was to use Tia from the Breakers series - believe it or not it's an almost exact match after some minor recoloring work, and the animations are on par with her fighting style too. Obviously that won't work for your project, but I'm sure there's some sprites out there that would do it.
So far as mechanics go, she'd be a middle grade fighter with some workable moves. Not quite the melee capability as say Wolverine, Colossus, or even absolute top end humans like Black Widow, but more than enough to hold her own. Her phasing would be a simple command (Ex: Attack + Jump) that turns it on or off. The effect makes her physically invincible (I debated whether certain beam or elemental effects might still hurt her) and reduces her falling speed so that she kind of floats in the air - but her attacks still hit normally (just assume she's making herself tangible for a split second).
While phased, the MP meter acts as a breath meter, constantly decreasing. If she runs out of breath, phasing ends, that simple.
The comics, shows, etc. explicitly state she does not become transparent, but I would still add a very minor transparency (using mode 6, and channel controls to make her about 85% opaque) as a visual clue to the player.
In addition to the above, I'd also planed to make her do extra damage to machines with all her moves, and have some of her normal moves takes advantage of phasing automatically. One example might be a throw where she starts by phasing her arm into someone for big damage, or even more if its a machine. Another might be phasing them into the ground and back out again (with them left there as a fatality if the damage is enough to KO them).
Honestly, IMO she's one of the more simplistic power sets to represent assuming you can find some matching sprites. Doubly so in your game since you've said you don't worry too much about balance.
DC
https://www.youtube.com/watch?v=TLVLYM83dxQ
