Rock Lover

The quest you want to do for this achievement is Lost In The Deeps, which is picked up by [npc=44945], after you are at least honored, with [faction=1171].
Pyrite stands and watches over the children, to your left if you use the portal from temple of earth, or in the first entrance you reach if you fly from the same.

This is a so called random daily, which means that everyday there is a chance of it being available. This quest shares group with Beneath the Surface and Underground Economy(the underground quests), so theoretically there is a 33.3% chance of it being available everyday. This means that in average it should take players 30 days of checking Therazane to get this quest 10 times, which most players would disagree with, so despite blizzards continuity, they seem to have make the quest chance "Uneven".

Another note is that all the underground quests, should be combined with Motes and Fear of Boring, since they all are in the crumbling depths.

A map for the pebble quest

Unfortunately the best way to get this achievement is to go check everyday(or as often as you please). Take the portal from Stormwind or Orgrimmar and then the portal to Therazane. (If you are hunting achievements, combine the checking with checking/doing Fungal Frenzy, Fungalophobia, My Very Own Broodmother and The Glop Family Line)
This is the only quest that [npc=44945] can give, so you can simply check if he have a quest everyday, and if he does, this is the quest you want.

Hope I shed some light! Cheers!

Got the achievement just now. I got mail that read:

The Postmaster - Recovered item

We recovered a lost item in the twisting nether and noted that it was yours.

Please find said object enclosed.

Poor Pebble... always getting lost...

The quest is not always available each day, it's random as I got the cave daily instead today.