There's no Karel level, actually. There's a Kenneth and a Jerme map, Karel and Harken can appear on both. I has something to do with how many doors you open before a certain turn, though I don't know the exact details.
That's only on Jerme's map, where opening two or fewer doors gets you Harken, and three or more gets Karel...I
think. On Kenneth's, it's how many promoted enemies you kill by a certain turn (8 sounds right for some reason). Three or more again will net you Karel, while two or fewer spawns a Harken.
EDIT: Oh, bah. Checked Serenes Forest - it's two or more promoted enemies or four or more doors to get Karel. And it's turn 10.