Beat the first four stages to clear the mine, and you will unlock this achievement as you enter the Jungle stages.
Since the levels are random, there's not much tips to give. Sometimes, the levels will be very hard and you won't even beat stage 2, and other times you'll beat all 4 in just a couple of minutes.
In order to unlock the shortcut to the Jungle, you need to meet the Tunnel Man by dying and starting the game over and beating the Mines three times. He will first ask for 1 bomb, then 1 rope and finally $10,000, then the shortcut opens up.