The time I got the Silver Sword to go critical was when I basically did a pseudo-Sigurd solo, using other units but basically always sending Sigurd forward as much as possible and having him do as much as he could every turn. Then Leg Ring Celice pretty much did the same thing as much as he could. It was pretty funny, I think it was at 100 kills by chapter 8 or so so Celice was just annihilating everything he touched.
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Mistake you're making - overlooking the fact that we might not want to be saved.