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You will need a fair bit of pre-planning for this.
For a few days go out collecting as much flammable stuff as you can, Fir/Cedar firewood are great for fires and are abundant through tree limbs which are infinite. Coal will be especially good here however there is a finite source of them (though there is more than enough that spawns in for it to not really matter). Breaking wooden furniture etc.

This HAS to be done with a campfire (no stoves or barrels) meaning you have to do it outside. So find a cave to stop the wind extinguishing it, move all your timber to said cave with enough food to wait it out and keep the fire lit.

The fire caps at 12 hours so putting more fuel on top of that is a waste. Go out and hunt for food in the meantime or sleep/pass the time.

Another thing you can try is doing it in a concealed place way from wind outside a cave where the temp drops below 0^oC. this will make the fuel burn longer and make it more efficient... If you want to be especially stingy with your fire supply.

This is also a great way to knock off another achievement called Beneath a Starry Sky which is basically survive 3 consecutive nights outside

Enjoy your 50 charcoal after you complete the achievement