After you've received the quest and fixed the mine cart with the oil you can move on to the next part of the mine.
There are 3 forklifts that you need to use to move pallets to help make bridges to get to the areas you need to go.

The first forklift is on the far left and you need to move the pallet (see pictured) to be able to reach the second forklift and pallet. NOTE: Space bar moves it left and right (horizontally) and the direction buttons move it up and down (vertically).





Go across the bridge you just created and over to the second forklift and move the pallet into position.





Now you can cross the bridge to the third forklift and position it to reach the next area (see pictured).





Go back to near where you entered the second area but instead of going left back to the mine cart, follow the ledge over to the right and cross the makeshift bridge and cross into the new area.

Follow the passage around until you come to the heart of the mountain and find that it's damaged.





Clicking on it also reveals the tune you need to play in order to get the broken piece so pay attention (or read ahead).

Go up the spiral ledge to the left and meet the guardian of the crystal who thinks you're a miner. Have a conversation with them.





From the crystal pictured, click middle left, far left, middle right, far right and the way to the passage opens up.





Congratulations, you've now found the missing piece of the heart of the mountain, and now all you need to do is join it with the broken crystal and you'll have your achievement!