WHY YOU WANT INVERTED GARMOTH'S HEART
An Inverted Garmoth's Heart is used on your Sub-weapon and Awakening Weapon to increase their stats. It also puts "Fiery" at the start of their name.
Sub-weapons: Max HP +150, Max Stamina +100, Special Attack Evasion Rate +10%
Awakening Weapons: Critical Hit Damage +3%, +2 Crystal Slots
As you can see, you will need 2 to 3 Inverted Garmoth's Heart for your main character's weapons.
To make it, you will need 1 Garmoth's Heart and 1 Inverted Energy, then use Heating to combine them. To get Garmoth's Heart, buy it or get lucky with the world boss drop. To get Inverted Energy, talk to Hughol in Duvencrune and accept the quest Inverting the Energy.
If you for some reason want to *make* a 2nd or 3rd or decide after reading this guide that you don't want to quest to get the 2nd one, talk to Hughol again to get another Inverted Energy.
HOW TO GET A FREE INVERTED GARMOTH'S HEART
Welcome to a very long questline. It isn't hard, just long.
In the Suggested Tab of your Quest Log (O), scroll down to [Combat] [Lv.60] Study the Time of Dragons for Inverted Heart of Garmoth.
The first quest should direct you to Black Eyeroot in the Crypt of Resting Thoughts. There, you'll accept the quest Orzeca's Records: Time of Dragons, after which 14 new quests will open up.
These 14 quests can be completed in any order and at the same time.
I highly recommend completing the ones labeled "Easy" right away, just to have them done, and then immediately plotting and setting up how you'll tackle Chapter 2.
[CHAPTER 1] STAR'S END'S ARTIFACT -- EASY
Give Fallen God's Ring.
Obtained from completing the quest [Star's End] Fallen God's Ring, part of the Star's End Storyline.
[CHAPTER 2] NOUVER'S REVERSE SCALES -- VERY, VERY, VERY LONG
Give 400 Nouver's Reverse Scales.
Obtained from defeating Nouver and Weekly quests.
Complete [Chapter 13] to unlock the Weekly quests that can get you a total of 7 of these a week.
Banish a character to stalk Nouver's spawns.
Banish other characters to stalk other bosses like Kzarka, Karanda, Kutum, and Garmoth.
Remind yourself that this is a super endgame item when you take a break from cursing the spawn times, so it's OK for it to be a marathon. Repeat that until you believe it. Or until you finish getting all 400. Whichever comes first!
[CHAPTER 3] PURE HUNGER -- MIDDISH-LENGTH
Give 70 Dark Spirit's Greed.
Obtained from completing Dark Rifts.
The actual time this will take will depend on how quickly Dark Rifts spawn for you. Hopefully you don't need them for Loot Scrolls.
[CHAPTER 4] IMMORTAL POWER -- CAN TAKE LONG
Give 50 Turo Heart.
Obtained from grinding at Tunkuta, which requires a party member and at least 270 AP.
[CHAPTER 5] PERFECT DARKNESS -- CAN TAKE LONG
Give 10,000 Corrupt Turasil Darkness.
Obtained from grinding at Thornwood Forest, which is done solo and requires at least 250 AP.
[CHAPTER 6] BREATH OF NATURE -- EASY
Give 100 each of Wind/Earth/Water/Tree Spirit Stone Fragments.
Obtained by grinding in Kamasylvia.
Wind Fragments: Navarn Steppe from Ferrica/Ferrina/Griffon/King Griffon
Earth Fragments: Tooth Fairy Forest, Loopy Tree Forest, and Navarn Steppe from Feather Wolves
Water Fragments: Manshaum Forest
Tree Fragments: Mirumok Ruins
[CHAPTER 7] ENDLESS MAGIC -- MIDDISH-LENGTH
Give 10 Hesed's Crystals.
Obtained via House 5 in Duvencrune.
Requires 11 Refined Black Energy Residue, which requires 25 Black Energy Residue each and is crafted in House 5 in Duvencrune.
In total you will need 275. Black Energy Residue drops from all mobs and you should naturally get this while grinding for Chapters 4, 5, & 6.
[CHAPTER 8] LATENT AURA -- EASY
Give 5 Concentrated Boss Aura.
Obtained by Heating any boss gear. The Auras must be the same type. You get 1 Aura for an unenhanced piece, 10 Auras for a PRI piece, 15 for DUO, 30 for TRI.
Just buy 5 unenhanced boss gears to finish this quickly.
[CHAPTER 9] HONEST ENHANCEMENT -- EASY
Give 100 Concentrated Magical Black Gem.
Obtained by using Simple Alchemy on: 5 Black Gems, 1 Sharp Black Crystal Shard, 1 Hard Black Crystal Shard.
Black Gems are made via Simple Alchemy with 1 Black Gem Fragment, 1 Black Stone (Weapon), 1 Black Stone (Armor).
Black Gem Fragments are looted from Gathering or Hunting.
Note: All of the above can be bought off the Central Market.
[CHAPTER 10] HOUR OF PURIFICATION -- EASY
Give 50 Magical Shards.
Obtained by Heating Yellow-grade Black Magic Crystals.
Just buy Sealed Black Magic Crystals from the Central Market.
[CHAPTER 11] BARBARIAN'S CAULDRON -- CAN TAKE LONG
Make 1,500 Alchemy Stone Shards.
Obtained by Grinding crafted Alchemy Stones.
(Click my profile to quickly find my guide for this)
[CHAPTER 12] CRYSTAL OF BALANCE -- EASY BUT SEMI-EXPENSIVE
Give 9 Cantarnia's Crystals.
Obtained from O'dyllita Chief Librarian Francia for 500m each. Total Cost is 4.5b.
[CHAPTER 13] ALLIANCE AND COOPERATION -- SUPER EASY
Talk to the dude in Narcion that the quest immediately takes you to.
Opens up Weekly Quests to get more Nouver Scales!
[CHAPTER 14] FAITH AND PROOF -- EASY
Reach Level 62 :)
WHAT'S NEXT? HOW TO APPLY IT TO YOUR GEAR
Have the weapon you will be applying your new Inverted Garmoth's Heart to in your inventory. Talk to your Black Spirit and click the Item Reform option. Click your Inverted Garmoth's Heart and the weapon you will be applying it to, then click Reform.
If you've applied it to your Awakening Weapon, don't forget to slot in crystals!
If you wish to remove it from your weapon(s), you must first remove the crystals.
Then go to Hughol in Duvencrune and buy Mirror of Equilibrium.
You do not need to "worry" about getting this until you have PEN Boss or similar weapons to apply it to, but it's better to start as soon as the questline opens for you.
First off, thanks for listing this so its nice and easy read. I didn't know about this quest before I saw this post, so I appreciate you making a guide for it.
A few things I ran into, which might be useful for other adventurers if included here.
Chapter 7: Requires 10 hesed's crystals, each requiring 11 refined black energy residue.
In turn, each refined black energy residue requires 25 black energy residue.
So to make 10 hesed crystals, you need 2750 black energy residue, not 275.
Chapter 8: I figured I would get a PRI boss item to get 10 concentrated boss aura's, as I would need some for the Star's End main quest as well. You can't heat enhanced boss gear. The numbers you listed for PRI/DUO/TRI only work for the named concentrated boss auras (i.e. Kzarka's or Karanda's) that are obtainable through simple alchemy. TLDR: You can only get these by heating base boss gear.
Guaranteed, not "free".