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Rock Lover
Complete the Lost in the Deeps daily quest in Deepholm 10 times.
Rock Lover is a 10-point achievement earned by completing the 'Lost in the Deeps' daily quest in Deepholm 10 times, rewarding the pet 
Pebble.
Reach Honored with Therazane
You must be at least Honored with Therazane before Pyrite Stonetender will offer you the 'Lost in the Deeps' quest.
Locate Pyrite Stonetender
Travel to Deepholm and find Pyrite Stonetender, who watches over the children near the entrance area — she is to your left when using the portal from the Temple of Earth, or the first NPC you reach when flying in from the same location.
Complete Lost in the Deeps 10 Times
'Lost in the Deeps' is a random daily that shares its rotation with two other underground quests (Beneath the Surface and Underground Economy), giving it roughly a 33% chance of being available on any given day — however, in practice the quest appears less frequently than that, so completing it 10 times will take well over 30 days.
Tips
This achievement is time-gated by a random daily rotation with approximately a 33% theoretical chance per day, meaning a minimum of 10 days but realistically significantly longer due to the quest appearing less frequently than expected.