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Defeated Kyrisa's Pet is a collection, that takes place within the Witches of Dathomir Theme Park on Dathomir.
You can start and complete this collection by completing the The Greater Good quest, which is part of the Corrupted Rancor storyline which is started by Fath H'ray for the Nightsisters or by Rancor Handler Izaryx for the Singing Mountain Clan.
You will need a group to complete this quest, as it is group content.
Reward: XP and the Rancor Euthanasia badge