After you have the shovel, (which you can get from
*** Spoiler - click to reveal ***the cave just West of the mountain spawn, it has three corpses stuck on pikes right outside it above some shallow water (you will need the rope gun and probably the rebreather as well to traverse the cave.)
) I'd recommend going up into the snowy mountains where there are fewer cannibals, situating yourself a bit to have sleep, food, and water figured out, then just digging away. This is especially easier if the season is currently winter, as I believe that also slows cannibal spawn rates. The fewer cannibals, the easier time it is to dig. From there just keep digging till the achievement pops.