It says just for one night.
Either way, with Minecraft's mechanics, this would still be easy so long as you knew the game.
From the basic rules we gather: hardcore so you can actually die also forces highest difficulty, must keep moving so that food actually becomes an issue, limited inventory space so you can't hoard all the nice things in your massive inventory, no shelter. The goal is to last 15 days and nights like this.
But so long as you can at least get an iron sword and maybe a leather helmet, that's enough to wreck any overworld mobs day and night, so long as you use either a second iron sword, or a few wooden swords to hunt cows and pigs with, an axe should you ever need more wooden swords.
Swords = 2 slots, helmet doesn't count, food = 2-3 slots (don't take chicken meat, zombie for emergencies), good to go. The hardest part will be the first 2 or 3 nights, of which you could use that one night shelter.
A bow would be nice too for taking care of skeletons, or larger groups.
