The Vision Quest badge is for "Spending 6 minutes at "full psychosis" (360 seconds)"
"Full psychosis" refers to when your Psyche bar (green one above your health) depletes completely. A good way to farm this is the first "Tough Love" trial as there is an enemy who will gas you, instantly putting you at full psychosis. Simply allow yourself to be gassed and recover before dying. Repeating this a dozen or so times to get the full 6 minutes.
Also two handy things to note:
1. The in-game badge menu tracks your progress.
2. Leaving a trial after gaining progress still counts towards it.
Video guide for reference: