The Breastplate of Resistance is found prospecting around Barney's house, i've personally seen it gotten the most riiight where i am in this picture, on the grass next to the lighthouse (if you're struggling just go here and reset your prospector over n over not digging if its not flashing nearby, digging only over here)

The Shield of Smiting is found fishing (in this islands only fishing spot lol)

The Rightful Boot is found fishing (can be found in either fishing spot)

The Sinister Boot is found fishing in the lake (the water past the stone arch)

The Girdle of Ogre Strength is found prospecting near the haunted ruins (the area where you grabbed the shinies for Yuki)

The Gauntlet of Righteousness is found prospecting anywhere on the island

The Helm of Brilliance is found fishing (in this islands only fishing spot)

The Gauntlet of Dexterity is found prospecting anywhere on the island (but ! i have seen it most near the dock where you spawn in)