Upgrade at the Work Bench and meet up with Ellie. She'll attempt to repair the huge drill miner, but still needs you to check on a few things. Kill off the Cysts ahead and grab the battery passed them. While around here be sure to grab an extra Power Node. Place the battery inside the machine and move up to the above level.
After dealing with a few Necromorphs, but nothing too serious. Pick up the circuit board and return to the machine. Hack it to restore power. Ellie will start the driller up, so climb on board. As you ride across the cave many different swarms of enemies will attack.
Ripper down any Slashers or Pukers that manage to reach you, while use the Plasma Cutter on the Lurkers that cling to the walls. If you can, push any enemies into the machine's drills to create some meaty splatter. When Ellie smashes through the cave wall the chapter will end.