Episode 3 picks up in the dugout by the furnace and chest. "Last episode was the first day and then the first night," Basket says, so this is day two in the hardcore world, and the zombie dungeon from the first episode is still waiting down the tunnel.
Into the zombie room
After a short trip outside for wood, where a spider turns up ("let's get some string. Or not."), Basket heads back down and digs toward the dungeon. The first idea is a careful one. "I'll be a little cheap and kill those guys from here just to thin them out before I actually run in there." Then Basket drops in anyway, and zombies crowd in close. The health bar falls fast. "Oh, man, I forgot I was on hardcore. Oh, that's a problem." Later Basket owns it: "I had forgotten that I was on hardcore and that I didn't have any armor yet," and came out "a little lower on health than I meant to."
Torches on the spawner
With the room clear, Basket covers the spawner in torches. "In case you didn't know, torches deactivate spawners." The dungeon chest holds a bucket, wheat and redstone among other things ("there was some redstone and a bucket and stuff"). Basket isn't in a hurry to farm it, since there's no need for "a lot of experience now until I actually get an enchanting table up," so the plan is to remember where it is and come back.
A marker and the last wool
Basket mines some more stone nearby, then climbs out and sets a cobblestone block with torches on top on the grass above, a marker "to find this place again." Out on the plains there are sheep again. One more kill and the count is right: "so now I have 3." There's pork from the pigs too. Across a river, a jungle rises out of the water, and Basket decides to go for it. "Let's actually set up a base in the jungle."
A bed in the treetops
The jungle has an ocelot ("Oh, a cat.") and an apple sitting on the leaves that Basket can't pick up because the inventory is full. With night coming, the safest spot looks like up. Basket chops into a tall jungle tree and loses the axe on the way ("there goes my axe"), then lays a plank platform high in the canopy with a torch on it, just as the sun sets. "It's a pretty big jungle." Up there Basket crafts the bed from the three wool and sets it down beside a crafting table.
Next time
The episode ends with Basket alive and lying in the new bed on the treetop platform, with the plan to scope out a spot for the main base from up there.