You need to throw the last hit on Zinogre, the one that will actually beat it, as it is afflicted with Blastblight, with an Ice-element weapon.
Unfortunately, if you decide farming for a Zinogre as soon as you first find it, those requirements will be very hard to achieve. To increase the chances of it doing so, you need to break as many parts as possible, throw a Paintball before beating it, and fulfil the pre-requisites that are unique to each Royal Monster. After you reach the area, initiate the fight with Zinogre and all that remains it to beat it and hope it retreats to its den.
