Moon Shell

In a nut shell here's theMoon Shell farm

Locations
>Gyala Hatchery (explorable area) (Leviathan Eyes, Claws & Mouths)
>Silent Surf (Leviathan Eyes & Mouths only)
>Rhea's Crater (Leviathan Claws & Mouths only)

Missions
>Zos Shivros Channel (Leviathan Eyes, Claws & Mouths)
>Boreas Seabed (Leviathan Claws only)

Where u choose to farm is up to u, I generally have always farmed them in the Gyala explorable area.. The Traveler will also be asking for Black Pearls eventually, and they drop there quite often.
However, there is also the chance for Azure Crests to drop in Rhea's and Silent Surf, which Nick will want eventually as well.

Wiki says: Since the Outcasts are hostile to others inhabitants, let them kill foes of no interest, except of course for the Leviathans you need to engage in order to obtain their drops. Careful pulling may be needed, as multiple mobs [in all listed areas] are close to each other.

U can generally use whatever solo farm build u like, the SoS works well. Just, as wiki says, watch your aggro, its easy to get caught up in a mass melee,
which,
u will lose.

The SoS solo build i used was;
>Painful Bond
>Vampirism
>Blood Song
>Shadowsong (FYI: blind criitters cant hit u)
>Signet of Spirits
>Mend Body and Soul (there will be conditions that u will want to remove)
>Armor of Unfeeling (necessary as with any SoS solo farm vs anything above level 10)
>Summon Spirits (using ur highest Luxon or Kurzick rank if u have the skill from both factions )

The Critters          
NOTE: All Leviathan are heavily vulnerable to blunt damage and highly resistant to piercing damage
>Leviathan Claw: (Warrior Level 24,15 Strength)
Skills: Distracting Blow, Irresistible Blow, Leviathan's Sweep, Primal Rage (elite)  
Armor ratings: Blunt damage=72, Piercing damage=152, Slashing damage=112, Elemental Damage=92
>Leviathan Eye: (Mesmer Level 24)
Skills: Clumsiness, Conjure Phantasm, Echo (elite), Ether Feast, Power Drain
Armor ratings: Blunt damage=32, Piercing damage=112, Slashing damage=72, Elemental Damage=72
>Leviathan Mouth: (Ranger Level 24)  
Skills: Hunter's Shot, Precision Shot, Quick Shot (elite), Storm Chaser, Troll Unguent
Armor ratings: Blunt damage=32, Piercing damage=112, Slashing damage=72, Elemental Damage=72
Notes: These creatures appear to deal chaos damage, despite using bow attack.

That's all,
Atty