The sad part is no matter how you complete this achievement, it is incredibly time consuming.
That being said, I believe the fastest way to get this achievement is using the Boomerang class. The Boomerang class's RB ability is to drop a bomb. Used correctly, this bomb can get you 250~ blocks every time.
First, dig straight down until you are very deep in the ground. Drop a bomb and throw a boomerang. Every time you throw a boomerang it reduces your cooldown time. Then, switch to build mode and dig straight forward like 3 depth. Throw your boomerang a second time and you'll have your bomb back. Rinse and repeat.
With this technique, you only have to repeat roughly 4000 times. It will take you around 9-12 hours of doing it repeatedly.