Digimon World: Dawn and Dusk/Find the Iron Pillow

To find the Iron Pillow for Kapurimon (or for... a Digimon in Dawn), you need to head in the direction you went in the first mission. Then, about halfway through, you'll see a Digimon and a wall. Talk to the Gizamon and he'll say that you need to battle him.

Gizamon is level 29, and his element is Aquan.

When you beat him, he'll give you the Iron Pillow!

After this quest, Gizamon will appear in that room. They digivolve into either IceDevimon or Raremon, and don't have an In-Training form.