Visit The Guy That Destroys Gems And Gives You The Item Back.
(Sitting Right Next To The Guy That Extracts Gems And Destroys The Item, In Major Hubs)
-He Has A Little Symbol Above His Head (A Gem With A Crack Through It)
Have Him Destroy 10 Different Socketable Gems And The Achievement Is Yours.
*Please Note*
You Must Get 10 Items To Socket Each Gem Into, As Socketing Them All Into The Same Item Does Not Count Towards Your Progress. Socketing Multiple Gems Into Something That Has Multiple Socket-Slots, Also Only Counts As One.
Good Luck!