Instructions
Enter World 2-2, at the Armor Spider's Archstone. At the end of this section, defeat Flamelurker and collect the Red Hot Demon's Soul. Enter World 4-3, at the Old Hero's Archstone. At the end of this section, defeat the Storm King, and collect the Storm Demon's Soul.
Upgrade a Short Sword, Long Sword, Knight Sword, Claymore, Bastard Sword or Great Sword to plus 8 with either Hardstone or Sharpstone fragments, which can be "farmed" from many enemies in Worlds 1 and 2.
Go to the beginning of 2-1 and find Blacksmith Ed's forge, near where the beggar sits. Give Blacksmith Ed the Red Hot Demon's Soul, so that he will forge weapons with Demon's Souls. Give him the plus-8 sword and Storm Demon's Soul, and he'll forge the Morion Blade.