He has not, actually. The biggest thing of note he's done since arriving here in Vatheon was helping Kratos repair Lloyd's key crest. I do believe he almost got in a fight with Lloyd once but he hasn't killed anyone, and that fight was nearly a year ago.

[He also got in a fight with Zelos once that Zelos never told her about. Shame on Zelos.]

Ah, Kratos is not here any longer, so don't worry about that. Thank the goddesses, that man was beyond irritating.