If you want to do this achievement legitimately, after beating the wither and making a beacon, you will need just over 23 stacks of minerals (iron/gold/diamond/emerald). This is to create 164 mineral blocks which can be mixed and matched to fully power the beacon. They are laid out in a pyramid under the beacon, as seen on the wiki:http://minecraft.gamepedia.com/Beacon
Iron is going to be your best bet for this as it is the most common. I dug all the way down to the highest bedrock layer then counted 6 blocks above this. This will put you at layer 11, the best layer for avoiding lava pools when mining.
The mining technique I use is called Windmill mining (http://minecraft.gamepedia.com/Tutorials/Mining#Windmill_min...
) and I find it to be extremely efficient. In about 20 minutes I had enough diamond to sustain constant diamond pickaxes, and I now have more than I will ever need so they will help towards the beacon pyramid.
If you can, enchant a diamond pick with efficiency III (you will earn enough xp mining diamond and coal, and smelting iron/gold) and from then on do not let it break
! Instead, use an anvil to keep repairing it. It's quicker to spend some iron on an anvil than using unenchanted diamond tools.
If you come across Fortune III while enchanting, try to save this pick for diamond veins and not waste it on stone.
I've been mining for a good few hours on a fresh world and I have 80 mineral blocks (mix of iron, gold and diamond) so it will take a long time! My current setup is a Efficiency IV Unbreaking III diamond pick (absolutely godly) and a Fortune III Unbreaking III pick for diamond and sometimes coal.