Hunt for Leviathan Souls is a mission in Tools of Destruction taking place near the spaceport on Cobalia. After reaching the spaceport, Ratchet met and talked to the Smuggler, who offered to buy his leviathan souls if he managed to find any.
Walkthrough[]
If you have not yet bought the Plasma Beasts weapon it is recommended to do so now. They act as mines and trigger when an enemy draws near, at which point to pop up and rush at them, dealing a lot of damage to anything in their path.
Once you are ready head for the cave entrance past the Smuggler's ship, and then head either left or right. Both paths meet at the end, so the choice does not matter. On the left is a large room with two smaller islands, both occupied by Cerullean swarmers and Cerullean centipedes, on the right is a single larger island with the same enemies.
Once you jump onto either island the basilisk leviathan will appear, so quickly get the enemies out of the way and deal with the leviathan as you did in "Defeat the Leviathan". They have more health than the first leviathan, but should otherwise fall quickly to your weapons. Once you have acquired both Souls you will gain the Giant Hunter skill point, and can sell them to the Smuggler for 2,000 bolts each. Alternatively you can keep them for later, as the Smuggler will offer more bolts for them later on.