From what I've gathered from playing, The 4 main skulls are awarded depending on if you kept the rift secure/didn't die. You lose some rift points when revived, which will instantly drop 1 of the skulls from "Rift points lost".
1 Skull is determined by if you beat the stage under par. (Which, from what I know, is never staged what "par" time is.)
Your score is then modified individually by things like combo count. I believe you get a higher chain multiplier if you kill or hit an enemy that was / is hit by a trap. Larger combo numbers are better, or course.
This is where the real beauty of trap design comes in; if you stagger your traps, you'll give time for various combos to occur, along with your own fighitng. The way to "perfect" this game would be to find out how to fastest kill the enemies, while maintaining a constant chain for the entire wave. 2nd most effective method, would just making the biggest combos you could, one after the other.
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A personal note:
I never expected the "Weaver" aspects that came in later, personally. And it was nice to see a mini-boss type monster turn up. I have to say the games scale grows SO much bigger than the demo hinted towards, that I actually think it'd be nice if the demo included a preview of some of the later stages... some of this stuff is incredibly overwhelming-looking at first glance, and I wouldn't have expected it, if not for having seen videos before release.