ASTRONEER

The minimum you will need:
Bunch of tethers, medium storage full of tethers.
Extras you may want to take:
A power source and a drill attachment if you’re on a planet with harder terrain.

Search the surface of the planet you’re on (this is easiest on Novus or Desolo) for any cave entrances, if none are nearby dig down into the ground until you reach the first cave layer, placing tethers as you go. Search this layer for any deeper tunnels but if none appear, dig down again. Repeat until you reach the mantle and you unlock this achievement.

Alternative method:
1) Take a tractor/medium/large rover with a drill attachment, sufficient power source (and batteries if you need them). Using your vehicle, keep drilling down until you reach the mantle layer.
Edit: You may also want to make yourself a paver and soil canisters, to traverse caves easier, however it is not necessary.

This ackhvievement has been fixed as of patch 1.0.13. Simply drill directly down in a tractor and trailer to the mantle layer.

Things you will need

Drill head 2 (or 3)
RTG (or at least medium power generator)
Tractor
Trailer
4 packagers so you can get your self and equipment back to the surface