The Headshot Master in 1:05
OMG, I beat Fortheseven['s highly unoptimized first run, probably]! That won't last, but I'll enjoy it before I get utterly destroyed.
Providence in Sapienza in 1:27
This wasn't as smooth as my test runs which involved beaning Mads in the middle of a public street with a propane tank without anyone noticing, but this also works.
The messed up part is, the game can track this; it knows if you've acid-destroyed bodies for The Heisenberg, and it knows Caruso can be ground up in a shredder for Weeding the Garden, and there's the Colorado one with the hay baler. They totally know when someone is killed or their body destroyed by those objects. But they don't have special kill conditions.