Just giving my experience because I had no idea about this and still don't really get it.
I'm playing on Death Incarnate and I've been playing extreme stealth mode, so after seeing the Panzerhund and riding it for about 5 seconds, I simply got off and continued playing the level as I was.
When I jumped into the Lower Sewers, which seems to be about 3/4, 5/6 of the way thru this level the achievement popped.
Never did anything but press B (Xbox) and get off the hound.