If you're struggling with this, remember: the longer you take the more predator encounters you need to deal with, and the more food you need to consume to stay alive. The faster you complete it, the less total food/water must be gathered.

Drop items to complete the challenge on the floor. Ruined meat items seem to be deleted in containers, but on the floor they are fine (not sure if already ruined items will still give credit, but if they ruin on the floor it is fine).

If you're struggling with bullets, remember both entrances to Mine #3 have lots of them, usually.

If you're struggling with oil, remember you can scrap Lanterns and get the oil from them. Scrap the lanterns with the most oil, and use the lantern with the least inside of it to complete the "lantern" requirement. A slower but assured way is to cook fish you catch (or if you find a raw fish in a village refrigerator).

Most of the required items are extremely easy, e.g. the sticks and bandages, so try to collect some of them as you go about and do other errands, rather than wasting time on them directly.

If you are lucky/unlucky enough to find a revolver, or a rifle and more than the 10 bullets you need for it, feel free to hunt with them. I'd recommend a deer or bear if you're brave. Remember to aim for the head/neck to one-shit it with a rifle, or with a revolver to follow it as it bleeds out.