Yeah I used the iaito but I think it has the same bleeding effect. I indeed saw some blood once or twice. The first phase (with the 2) is really hit or miss, it's really easy imo to take down the fat guy as long as you know where his pal is.
Once ornstein is alone, and with the lightning ring equiped, you just have to be cautious, the good old hit and run technique, and watch out for his zone attack (which fucked me the first time as I didn't know he has one until the very end of the fight).
Now I can do teleportation yay, end of an era.