well, since no one's replied yet i'll take a stab at this. natural born killers is a file that i really don't have a good feel for, so take my comments with a grain of salt.
I'll start with a summary since my post is long-ish, and in case you don't read the whole thing:
Not really sure what a good general philosophy of Natural Born Killers is. I would assume play hellsmoke and Priestess sooner than later, then Igina. Lay off the grims (NO unnecessary Pure Terror; I'm gonna be watching for that next replay you post :p), except maybe Death's Embrace which seems to be working well for you. Pay attention to synergy with your SS's. Your opponent completely neglects this synergy with his own SS's and makes a lot of poor plays by not setting up a better synergy (which is key to refess) when his SS's had his back. This happens to you also on the warning knife turn, since the Angry Mob had you covered already.
Acolyte (or folrart shield knight) + Safiria is a standard refess open. I think if you drop Lebeau turn 2 you really put him in a tight spot since he WILL kill the acolyte. It's nice to go before Safiria can perform her engage skill. So for example: Lebeau does 40 damage - if saf attacks, the close skill will kill acolyte. Or, if she rests and acolyte rests, he'll get HP + 11 or 12. Next turn he heals for 20. Lebeau kills him anyway. going the first option means you'll lose lebeau each turn, but refess gets uncomfortable without its tank in front. plus you'll lock down his sp with him reviving acolyte all the time. if you play shade after lebeau you should be in good shape to play level 3's for awhile and most likely you'll sap one of his sp in the process. Or if you play Mindsoldier turn 3 I think he'd have a lot of problems too. actually I think I'm preferring Mindsoldier right now to keep the pressure on.
opponent doesn't need to be playing priest of the holy word so soon. boy combat priest should also not be making a cameo. wisp + Captain makes more sense. Wisp will allow the acolyte to stay alive for, like, one extra turn. but he needs his lvl three's out first. Paladin wouldn't be a bad choice to follow Captain, to try and get lucky against Hellsmoke, and also to kill everyone else and provide more tankiness. Priest can come out later. Opponent's SS's aren't too shabby; the engage mechanics should give him the time he needs to establish a field. Unfortunately he doesn't take full advantage of how much time his SS's allow him to set up a cohesive field.
Once again Death's Embrace is well timed to remove his tank. Good stuff. I'm becoming more of a fan of this maneuver every time I see you play it!
Dual-Wielding Soldier is far too squishy for him to be fielding right now, and he's not using that skill of hers any time soon. As a result, Pure Terror is pure unnecessary.
You seem to like that card, but there really aren't that many instances in Crest where it needs to be played. I would play Priestess of Madness first. Then play Igina.
Opponent does NOT need to be playing Blessing, although by this point it's a lost cause. He needs to establish a field again. Refess is all about synergy, of which there isn't much going on here.
Why warning knife?? Your SS is already going to handle Safiria; crest mindsoldier and smoke would have easily done the rest. Waste of a grim and also an opportunity to play a unit.