To get this achievement you need to reach the bottom of the mines in the Mountains found north of your farm.
The Mines can be opened while on the chapter spent getting the Third Stone Tablet for the Lighthouse. Once you've fixed Gus's Smithy and the Mines entrance you can enter the mines and start digging, additionally you will need the Hammer from Gus to break the ores.
The mines go down to Level 100, to progress through each level, you need to till the ground using your hoe to find a ladder.
Every floor you reach that ends in a 1 or 6 (6, 11, 16, 21 etc) is treated like a checkpoint so you can carry on digging from those levels rather from the top every time.
Tips: The ladder will never be found in the center of the level, it's either at the edge or very close to it, so start by tilling round the outside and work your way in to save stamina.
Also, to break ores from levels 31-60 you will need the "Expert Hammer" and to break ores from 61+ you will need the "Master Hammer"