If you want to get the Top tier Gem, the first thing to do is:
Find the caravan of orcs (white arrows on the minimap) sometimes killing them drop silver coins or gems.
Find Monuments and destroy them (monuments only drops gems)
Second thing to do is:
combine 3 gems of the same type in your inventary
Phase 1: x3 Normal Gems = 1 Carved Gem
Phase 2: x3 Carved Gems = 1 Polished Gem
Phase 3: x3 Polished Gems = 1 Refined Gem
Phase 4: x 3 Refined Gems = 1 Perfect Gem
Phase Final: Unlock your achievement