A combination of
Sweet Rvng's solution and
reforc3's solution over at TA.
The mutators to not starve and not take damage can be used to get all achievements in this game. All 25 quests have to be done in one playthrough / game. If you die, it will reset your progress. The Inventory mutator can also be used, however sometimes it's buggy.
A list of the challenges has been made by
Steam user Vic=HKC= and can be found here.If you have access to a laptop/tablet/etc., go to the page above and then CTRL + F to quickly navigate the quests by name. This will really help out for ones that need you to go to a certain area (taking a shower, making the water course deadly, etc.) with little time for looking around.
Also, to make this really easy you can use the Wheel Goat mutator from the MMO DLC which you get from this achievement:
The Wheel Goat mutator stops all time including the quest timer. So you can freeze time, find what you are looking for, and unfreeze time before completing the task. You can kill zombies while time is frozen, however you can't move objects while time is frozen.