SteamWorld Dig

The Old World is past a few blocks that require the Drill from Cave III. In this cave, you need to head to the hit a switch in three locations. In the top left, platform around some crawlers with the switch at the top. At the bottom left, you need to fight (or run past) some turtles and back, and in the right, you need to drop a few massive rocks to clear the path to the switch. After each switch, the camera will zoom back to the central area where doors are opening. Return there, follow the path and get the drill. Back outside, drill through those blocks and reach the Old World.

Achievement pops as soon as you enter the second area. There's water on the top right side that regenerates every time you re-enter, and the pipe in the central platform will take you back to Tumbleton.