Given that Herriman's arm was already on the rise and more than halfway to the needed location before Mifune even started moving, I've gotta agree with Dag. At least on the chain-launching aspect. 

And while Mifune's sword, when unhindered by the bulk of a chain, may be able to break the sound barrier, Mifune himself is NOT faster than a bullet (unless you're referring to bullets of a very slow sub-sonic variety).