To unlock this achievement, you must find a gem while mining ore. Ore veins can be found throughout the world of Aurai, but are naturally more prevalent within caves. Given that caves and dungeons are a prominent feature in each region, you should have no trouble encountering numerous ore veins with a high chance of mining a gem. You will need a pick axe to mine the veins.
Note: If you are having trouble locating an appropriate ore vein, go to the Conflux Mountain in the centre of the region of Chersonese. Once inside, you will find plenty of ore veins and are almost guaranteed to mine a gem if you stick with it.