Unearthly Apothecary is a Hidden/Silver Trophy which requires you to obtain an Elixir.
Yes, just a single Elixir.
Collecting a single Elixir does not sound like a daunting task but believe me, it can even cost you all of your playthrough fortune.
Lightning Returns: Final Fantasy XIII Elixir
what are Elixirs
Those of you who do not know, Elixir are very rare items which are capable of restoring all of your HP, ATB, GP and buffing you up with Bravery, Faith, Protect, Haste, and Shell.
The Elixir can be obtained either by buying them or by spending in Soul Seeds.
How to Buy Elixir
If you are planning on purchasing an Elixir, make sure that you have around whooping 360,000 Gil at your disposal.
Once you have this much money, you can travel to an Outworld Service NPC and buy them. But how to get such big bucks is the real question?
Please refer to my Monster Bane Trophy Guide to know more about the Ultimate Lair. For a quick overview, the UL is the last dungeon of the game which appears after you have completed the game and have done more than 50 side-quests.
This dungeon have 33 floors crawling with enemies, Last Ones (Omegas) and Treasure Boxes. Clearing out the Ultimate Lair will surely provide you enough Gils to make a purchase.
Honestly speaking, I would not recommend doing this at all! Such big Gils can be spent on other important stuff rather than an Elixir.