Quality Time with Snatcher is a challenge in Death Wish Mode. In it, you must survive The Snatcher for at least 2 minutes. He is completely invincible in this challenge, as he won't throw any blue potions, unlike last time.
In this level, as stated, the player must try to go through the Snatcher fight again, but this time, he cannot be hurt, and is constantly invincible. The player's goal is to survive this fight for 2 to 6 minutes, depending on how much effort the player plans on putting in.
All these bonus challenges do is increase the amount of time the player must survive the Snatcher for. Despite their simplicity, they can still be hard to achieve.