|N version||1.4 and later|
Jump to the right, and double jump against the corner. After you hit the walljump the third time, leap over to the door platform. If you lose too much momemtum, you will miss completely; if you have too much, you will collide against the ceiling and bounce into the mine. (a little bit of practice will help you adjust here). Jump and grab some gold, then leap over to the left side.
(the drone positions are crucial to this level) Hang onto this portion of the wall, and watch as one drone approaches you from the top side and another drone approaches you from the bottom side. When the bottom drone gets directly below you, jump off the wall, right past the bottom drone, and land below it at the entrance of the tunnel. Quickly run into the tunnel, as the drone that started on the top will be pursuing you.
Wait for the drone below to move away, then drop down and grab the exit switch. Stay in that little depression to the right until both drones go past, then follow the drone heading left into a second depression (both depressions are safe from the drone).
If you are feeling confident, as soon as the drone you are following leaves, notice the rest of the chimney upwards is completely empty; use this opportunity to jump up and chimney up to the top, and then jump to the door. Congratulations on completing the 70s column!
Otherwise, if you need to catch your breath, just stay in the little depression and wait for the drones on the bottom to revolve around twice (or for that matter 4 times, etc). There will be a clearing each time; use the strategy from above, and just chimeny all the way to the top. Follow the top drone out, and then jump to the exit. Congrats again!
Method 2 (Highscore)
Double jump against the first curve to get straight to the tunnel entrance; this will save a huge amount of time.