The title is slightly misleading, you don't not have to find some random underground diamond ore and mine it with iron tools in order to get the achievement, you only need to obtain diamond.

In the Tutorial World, there is a desert temple with chests containing diamonds. The co-ordinates of the temple are; X: -310, Y:66, Z:105. Saves the hassle of you finding the ore, additionally if you don't get the achievement from picking up the diamond from the chest, drop it and pick it up again.

I you need any help feel free to PM me.