How is the score calculated, and what actions can lead to higher scores?
There seem to be two multipliers in challenge. The flat bar on the left is your personal multiplier; goes up when you kill, goes down when you die. Maxes at 5x. The smaller circle is time in the current wave; resets to 5x for each new wave, slowly decreases over time. The larger circle is the combination of the two - personal multiplier x wave multiplier.
Based on this, you get the best multiplier when: a) you dont die so your personal multiplier stays high, and b) you kill big targets early in the wave, or finish the whole wave quickly so you get 25x points on everything or at least the high-value targets.
I /think/ that any damage not done by you directly (i.e. vortex/summoned dead/elementals/crash to desktop and possibly goblin bomb explosions) doesnt add to your score. I believe lightning bolt works (and often gets overkill!) but it's slow and dangerous in multiplayer.
Hope this helps!