Niffelheim

You collect Golden Ore by mining it down in the underground caves. You won't reach Gold until you hit roughly 20 floors down and even then, it's still rare to see it. It's unlikely you'll find large sections of it (as compared to Iron, Titanium and Copper) so you want to make sure you're keeping an eye for it any time you go down that low in the mines.

Be sure to remember where it was you collected the ore! When an Earthquake happens (every about 15-16 Days), the mines will reset and fill back up with rock and ore. All of the ore you collected previously will be in the same location as it was when you first picked it up, providing you remember where you grabbed it initially, you'll be able to farm the ore again. Because of this, you should place a Portal Scroll down near where you found some Gold Ore. The Scrolls create a Portal leading from wherever you placed it in the cave and one Portal in your Workstation area. This will allow you to easily travel back and forth and, when the Earthquake does happen, you'll easily be able to go back down to the floors needed to get the rest of the ore you need.

Getting to 100 will depend on your luck with how often the ore appears in the caves. If you're being diligent about upgrading your buildings, you'll need to start farming for Gold pretty early on in the game so you'll more than likely earn this before you hit 100 days played. If you're taking your time with the upgrades, this will take you longer to get as you won't be needing Golden Ore nearly as much.

Either way, once you have collected your 100th piece, the trophy will unlock. You do not need to have 100 on you at one time. This is cumulative.