The Female Dragonfly is one of the 24 Golden Bugs that can found in The Legend of Zelda: Twilight Princess. The Female Dragonfly can be given to Agitha for a Rupee prize. Once all 24 Golden Bugs have been collected, Agitha will give Link the Giant Wallet, a massive wallet that can hold up to 1000 rupees.
The Female Dragonfly can be found in Zora's River, right next to Iza's Rapid Ride Shop. Once Link is standing near the door, he can use the Gale Boomerang to bring the Female Dragonfly to him. The Male Dragonfly can be found in Zora's Domain.