WARNING: This is updated for NEW Survival Mode.
My character of choice for this run was Rashid, and I was mostly abusing the Eagle Spike Kick, and this is pretty common practice among the pros. You're basically going to hit it, jump back, and keep doing it. This is a rather flashy run, this includes a lot of Double Downs (some people might consider it quite arrogant, warning), but I did this with no Attack Ups or items to make it easier.
If you're planning on using items, bosses are good targets. But generally, as you get better at this mode, you should be able to farm items here with Rashid to take to higher areas.
Also, just like with the Evil Ryu/Gouken/Oni achievements from USF4, you can use the Matchfinder to save your behind if you get into trouble. That's how I beat it with characters other than Rashid.
No commentary yet, will update when commentary is added, but for now, here's the video: