Cactuar Island is a small island located south of Esthar; it is recognizable by it being a desert with a randomly appearing (and disappearing) cactus. This "Cactus" is the Jumbo Cactuar, a cactuar that has grown to an immense size.
Defeating this Jumbo Cactuar will lead to it joining you as a Guardian Force.
This island is available to you on Disc 3 when you have the Ragnarok.
This quest is available until Disc 4 (Return via Portal)