Instructions
Get more shards of hardstone. If you have come across just one, you will need at least four more. You can purchase more from the Filthy Man in world 2-2. If you killed him in the previous world, you must farm it by defeating phalangeals in worlds 1-1 and 1-2.
Return to the Nexus, which is your starting area. While you can visit Blacksmith Ed in the tunnels of 2-1, his upgrades are for stones better than hardstone.
Visit Blacksmith Boldwin in the Nexus, who specializes in low level upgrades.
Select the weapon you want to upgrade. If you have enough shards of hardstone on you, he automatically upgrades the weapon and gives it to you. Otherwise, he will tell you to go and get more.