Haven't completed this one yet, but so far it seems that you should finish the entire game first and then come back to get the PERFECTION ratings. As you go through the game, you get various equipment pieces and weapons upgrades that will help you get better times. Less time spent pounding any given enemy or obstacle makes you that much faster.
That has made it much easier to get Perfections. On some levels where I was missing it by a few seconds, I blew past it with tens of seconds to spare.