This comes just by playing the game. I have defeated about 150 guardians in 3 hours, playing just arcade mode and about 5 Guardian Rush bonus mode games.
I'd like to fix your guide Spiffing WotWot, you get overkill mode by reaching level 20 in arcade mode. NOT by killing 20 guardians..
The easiest way to get overkill mode is by playing arcade mode on easy.