Princess Parasol is Agitha's Level 3 Parasol from Hyrule Warriors and Hyrule Warriors Legends. It is described as the beloved parasol of the Insect Kingdom's Princess.
Interestingly, the Princess Parasol matches Agitha's "Standard Outfit (Twilight)", her unlockable Sweet Lolita recolor from the Twilight Princess DLC.
Level 4 Parasol
In Hyrule Warriors Legends, there is a stronger Level 4 version called Princess Parasol +.
Render of Agitha (Standard Outfit - Twilight) wielding her Princess Parasol from Hyrule Warriors