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Iron to Vendor Gold
Craft each of the following Philosopher's Stones.
Iron to Vendor Gold is a 5-point achievement that requires an Alchemist to craft one of every Philosopher's Stone across multiple expansions, from Classic through Battle for Azeroth.
Learn Classic Philosopher's Stone Recipe
Purchase 
Recipe: Philosopher's Stone from Alchemist Pestlezugg in Tanaris. This recipe requires Classic Alchemy skill level 50.
Learn Alchemist Stone Recipe
Purchase Recipe: Alchemist Stone from Almaador in Shattrath City. This requires Outland Alchemy skill level 50 and Revered reputation with The Sha'tar. Running Botanica repeatedly is a fast way to earn Sha'tar reputation.
Earn Shattered Sun Exalted
Purchase Recipe: Guardian's Alchemist Stone and Recipe: Sorcerer's Alchemist Stone from Eldara Dawnrunner, both requiring Outland Alchemy skill level 75 and Exalted reputation with the Shattered Sun Offensive. Running Heroic dungeons once and then grinding Normal mode is an efficient way to reach Exalted.
Craft Each Outland Stone
Once you have the recipes, craft 
Alchemist Stone first if it is required as a component for other stones, and hold off on vendoring it until you have confirmed it is not needed for a subsequent craft. Some stones require previous stones as reagents, so check each recipe before vendoring.
Obtain Legion Stone Recipes
Purchase 
Recipe: Infernal Alchemist Stone and Recipe: Astral Alchemist Stone as needed. You will need 
Primal Sargerite, which drops from Greater Invasions in the Broken Isles, with approximately 5 dropping per Greater Invasion completed. A short quest chain is required to unlock the Argus Alchemist Stone recipe.
Craft Battle for Azeroth Stones
For BfA trinkets requiring 
Hydrocore and Tidalcore, craft the Tidalcore version first since Tidalcore drops exclusively from Mythic Dungeons. After crafting, scrap the item at the Scrapper to recover all 15 Tidalcores, then convert them into Hydrocores so you only need to farm 15 total instead of 30.
Tips
Hold off on vendoring
Philosopher's Stone and Alchemist Stone until you have confirmed they are not required as reagents for a subsequent stone on the achievement list.Craft the Tidalcore BfA trinket before the Hydrocore version and scrap it afterward to recover your Tidalcores and convert them, reducing total Mythic Dungeon farming required.