You need to beat the game once to get this achievement, and then start a new game in achievement mode. However, all progress earned in previous saves carry over to the new save.
For this achievement, you need to collect 100 stones over any number of saves. You will most likely end up getting this achievement through normal gameplay, but if you're struggling to get it, upgrade your drill as much as possible and strip mine the top layers of the garden, as stone only spawns for the first 20 or so meters.