So, there are two ways I found to avoid being killed.
The Hard Way
It is actually possible to dodge most of the hits using slide. I say most because I wasn't ever able to miss the last couple hits, which will still leave you at half health. Right when you see the animation start, and he raises his sword in the air, run away. If you are too close to him, you will get knocked into the air and it will be a KO combo (on proud mode at least). You'll need some practice to get the timing right, but just before he disappears to rush you, slide away. And keep sliding around because your life depends on it. Eventually, the timing changes and he ends up hitting you just after you get out of a slide so you will get the last few hits, and it left me at about half health. You could probably time it right to not have that happen, but I couldn't ever get it right.
The (Kinda) Cheap Way
I don't like this way. It feels cheap to me. But it is honestly the easiest way and the way I ended up beating him. Make sure you have a fully leveled (level 4 or 5) shotlock command in your arsenal. Any less and you'll still end up taking the brunt of the attack. As soon as he pauses to do it, right when the animation starts, hold down R + L to start a shotlock. Lock on and, just before he attacks, hit X to start your shot lock. This will make it so that he can't hit you, and you should be doing damage to him as well. If you were able to get it maxed out, you'll last throughout the entire move and even be able to do quite a bit of damage. And even if you didn't you should survive the attack.