Scattering

Scattering is one of the few known ways to truly defeat an immortal.

As immortal beings, @Primordials, @Titans and @Olympian Gods can't be killed. Even if they are cut up into many pieces, they can still survive and eventually rebuild themselves over time, especially if they possess a healthy host, as was shown with @Kronos although this is different than scattering as only Kronos' physical form was destroyed.

The process of scattering is where the being in question receives a powerful blow that would destroy a mortal being utterly but where they can survive as an immortal. This destroys their physical form and scatters their essence to such an extent that it is believed that they won't ever be able to form a consciousness again, let alone a body. Thus they are scattered and harmless, though they aren't dead. If they are already weakened, the process is much easier, as was shown when Kronos was scattered by being removed out of @Luke Castellan's body with a @Celestial Bronze Knife. It was suggested that Luke's body was holding Kronos' essence together after he was possessed, possibly explaining why this happened.

It appears that a scattered immortal's essence may be sent to @Tartarus. @Percy Jackson wondered if pieces of Kronos' essence were floating around and laughing at him as Percy and @Annabeth Chase traveled through the realm. @Koios also stated that Kronos' essence was so scattered that even the regenerative power of Tartarus couldn't heal his injuries.

It should be noted that there are a few other ways to permanently defeat an immortal. For instance it is shown that an immortal's essence can be absorbed by a more powerful immortal (an example being when Krios and Hyperion's essences were sucked into Tartarus) or even a ghost using the correct spells.