Killing Spirits?

Many in the past have wondered: is it possible to kill a spirit? They are metaphysical entities, yes, but mankind is ambitious, persistent, and ingenious. It is not unthinkable that a spirit could become twisted, malevolent, and powerful enough to threaten a human settlement; in such an instance, it would need to be destroyed.
Records exist of events in which a spirit had manifested too close to a settlement, and the townspeople were forced to act. In these circumstances, either the spirit was forced back into its realm by the intervention of powerful druids or shamans, or a bargain was struck to ensure peace between the spirit and the settlement.
However, some groups - adventuring parties, primarily - claim to have killed spirits. These stories have not been confirmed or verified, and they are easily twisted into tall tales, but some people nevertheless believe it could be possible.

Killing a Spirit

According to those who claim to have done it, the first step to killing a spirit involves destroying its anchor. This is the point in the physical world that the spirit asserts control over. For instance, if one wanted to kill a spirit that has manifested around a centuries-old redwood tree, the tree must be chopped down, burned, or otherwise destroyed. Naturally, the spirit will not take kindly to such aggression, and will defend itself with lethal force.
After the anchor is destroyed, the spirit will be ripped from its realm and into the physical world. The next step is to kill the spirit's corporeal manifestation, but this is where the task may be impossible. Spirits are immensely powerful even when confined to an anchor, and this requires the erstwhile spirit-killers to fight an unconstrained spirit. Such a being may be literally immortal, even to the most skilled warrior in all of Saekai.
Suppose the spirit is mortal, however, and a mortal blow is struck to it. The being has been eliminated, but its energy will disperse and the spirit may rise again after some time (even though this may be many centuries). In order to permanently banish it from the world, the being must be banished by a druidic ritual, or devoured by another spirit such as a hunter's companion.
Of course, because all adventurers' stories must end with a hint of treasure, it's said that the spirits' energy will disperse and flow into the group that killed it, permanently lending them great strength.

Cymere?

In the tale of Fallow Point, Lasang uses Cymere to strike down Tallu and Takai in what should have been a wildly unfair fight. If Cymere worked to kill gods, surely it could kill a spirit.
Indeed, a legend of this exists, although it's in the form of a bardic ballad and its authenticity is therefore dubious. The ballad details the adventure of a cunning Bayinae man named Varili, who killed an all-seeing spirit threatening his village. Varili approached it with a hunk of Cymere, but was able to trick it into believing that he wasn't carrying anything, as the spirit was blind to the Cymere. According to the ballad, simply touching the crystal to the spirit's body immediately reduced the being to ash.