Lemme throw you some feedback real quick...
Lore: A little... shaky. Seems a bit scattered. Then again, this is the most subjective part of a champion, so pay me no heed.
Passive: Simple, but effective--essentially an upgraded version of Katarina's Killer Instinct. This is one of those abilities I'd call "sensitive", because you'd be hard pressed to make good numbers on this one--either they'd be a teensy too high and make it broken, or a teensy bit low and completely useless. I imagine you could come up with a better ability than that, but for the time being it gets the job done.
Phase Shift: Cool ability... hard to use properly, but that could be a good thing. My only concern would be in making it too hard to use, but that's a hard thing to do. For now, thumbs up.
Corrosive Aura: Not a fan. Generally, random effects whose odds can't be modified through gear are undesirable--in a skill-based game, players savor predictability, because that implies adaptability--both in using and in defending against. Consider how many complaints have been made against Gangplank's Cannon Barrage in all stages of its development: too powerful if you get lucky, downright useless if you don't. Generally not a desireable combination of abilities. In addition, I don't see much synergy between this and his other abilities.
Anti-Matter: I see you wanted to make an AoE move for both mass nuking and farming, but you have a slight oversight, in that the instant-kill effect is pointless; at lower ranks, the chance of getting an instant kill is miserably low, but at higher levels, the damage (accounting for AP scaling) is high enough to kill any minion outright. I can deal with the instant-minion-kill mechanic because it exists on Master Yi's Alpha Strike, but the effect is much stronger there.
Rift From The Void: Numbers aside, I don't really see how this effect brings much to the table. It's essentially a weaker version of Twisted Fate's Gate, with Kassadin's Rift Walk duct-taped to it. Since you don't specify whether this champion is supposed to be a caster or a fighter, I can only assume it's both, as is the case with Kassadin or Nunu. In either case, I can't see myself really wanting to use this skill very often--it's more likely to deliver you into a trap with just the teleport, but the ability to deliver a large amount of true damage over the largest area-of-effect in the game makes it very risky balance-wise.
Is this champion supposed to be a caster, or a DPS? It feels like you're trying to accomplish too much with one champion--generally not a winning formula. A versatile skill set and a focused one are not mutually exclusive--right now, you have plenty of the former, but not the latter. To improve this champion, I would sit down and focus on what you want this champion to accomplish. What would you want to do with him if you were playing him in a game? What roles should he play, and what roles shouldn't he? How would you build him? From these questions, you might figure out what you should do with your skills, and even come up with new ideas. In any case, good luck!