The quest is unlocked after completing the Versus Calamity Ganon challenge.
"Calamity Ganon craves the power of a four-legged beast. It falls upon you to feed this hunger or leave the appetite unanswered."
"By absorbing Malice from a Lynel, Calamity Ganon gained an unnatural new power..."
- Calamity Ganon: Bonus Combo