"Imbue your attacks with THROAK TENTACLE POWERS! Grants a 10% chance on melee attack to deal ice damage."
The Shivly is a trinket that when equipped to one of the 4 Trinket slots in the character panel, and provides a passive bonus. The Shivly will give Flux's attacks a 10% chance to cause ice damage. Ice damage slows the target, unless it is resistant against freezing, like boss monsters and Throaks.
The recipe for this trinket is found in the Conspicuous Outpost in the Bawg's Grandmammy quest line.