Took me a bunch of tries, but I finally beat him with Jin and War Machine. Play defensive with Jin on phase 1, use Bloodia Punch if you must. When you get to phase 2, War Machine's War Destroyer kicks ass. It's an aerial attack that hits while going up (if he's right above you) and coming down (relatively homed in on his position). War Machine's shoulder cannon is also pretty good to play if he's on the other side of the stage.
For a helper character, I used Iceman. He drops ice on screen. If Onslaught is right on top of you, it'll hit. Thor also works in this situation.
It's also worth restating that it took me a LOT of tries. Onslaught was designed to be insanely unfair. After all, it was a Quarter muncher back in the day. I probably would have spent $15 in Quarters getting to and beating Onslaught. I got so close a bunch of times before I got him.