Location: Great Sandy Desert
Petitioner: Girl Waiting for Father, Mitt
Reward: Mitt's Ring, 500 Berries
Objective Reward: Power Resistance +15 Ring

To trigger this Side Story you must first rid Alabasta of Crocodile and return to Waford. Once you've liberated Alubarna and gone back to the real world the main story will swiftly kick you back into Alabasta for a bit, and you can explore old areas to find new quests. Night Exterminator is one of them, and you'll find the petitioner, Mitt, in the Sandy Oasis. It's at the north end of Great Sandy Desert. Mitt is standing beside the southern bridge out of the oasis.

Mitt is waiting for her father to come home, but the nightly appearance of deadly Deluck Brothers, a group of powerful scorpions, have stymied any such reunion. She pleads with Zoro to get rid of ten of the things the next time the sun goes down. (And Sanji, of course, will jump in to steal Zoro's spotlight.)

Head to the campsite in the middle of the oasis, settle down for the night, and then choose to rest until night when partying. Head out into Great Sandy Desert once the sun has gone down and you'll occasionally see Deluck Brothers wandering the wastes. You can tell them apart from the other scorpions thanks to their distinct blue exoskeletons. They're Technique fighters, like the other scorpions in the desert, and only a bit more difficult.

(And, ironically, you shouldn't be fighting these things with either Zoro or especially Sanji. Let Nami and Usopp do most of the work.)

Defeat ten Deluck Brothers (three battles' worth, four per battle), then return to Mitt to end the Side Story and receive your reward.