A Leviathan Soul was the soul of a large and dangerous creature, like a Basilisk Leviathan, and could be acquired by killing such a creature. Leviathan Souls were valuable in the Polaris galaxy, and could be traded for large sums of bolts. Grunthors also possessed Leviathan Souls.
Behind the scenes
If you use a Groovitron on a Grunthor on Sargasso and slowly push the Grunthor off a ledge while it was dancing, mass amounts of Souls will be given to the player while the game was killing it multiple times. As an added bonus, the game didn't mark them as dead, so that it could be repeated. 
- Ratchet & Clank Future: Tools of Destruction (first appearance)