This one you can pretty much only get in Aquania. Make sure to use omega builds (you need to use the whip-credit to email@example.com) on Biowulf and the Octo-Brain whenever possible, and you should have no problem. After defeating the Octo-Brain, it is important to note that the cutscene where Breach pulls you into her pocket dimension does add about 15 seconds onto your time.
In Abyssus, if you quit to the dashboard, the timer will reset but place you where you were in the level (credit to firstname.lastname@example.org and Tyger7)
The glitch may happen possibly in other random worlds. The last level as also glitched and stayed at 0 time after a death and reload. Not 100% certain on if it's luck or can be forced.