Once in Giddeus, take all left-hand turns. You will eventually end up at H-7, where you will see a Yagudo NPC named Laa Mozi standing at the mouth of a cave entrance. Talk with him and he will take your Food Offering.
Return to the entrance of the zone. This time, take all right-hand turns until you get to G-7. (You will have to cross a stream at one point.)
You will soon see Ghoo Pakya standing at the mouth of a cave entrance. Talk to him and he will take your Drink Offering.
Return to the roof of the Rhinostery in Windurst Waters and another cutscene will appear when you reach the top of the stairs. Afterwards, report back to the Windurst Gate Guard to complete the mission.
Some users have been able to finish the mission immediately by talking to Leepe-Hoppe; others have encountered the same dialogue they received before leaving for Giddeus, only to return the next day (after the JP Midnight server reset), speak to Leepe-Hoppe, and find themselves able to at last finish the mission. It is unclear what causes this issue.
A level 12 job can complete this mission with no aggro. A level 10 job will get some aggro, but all of the beasts will check Easy Prey.
Receive two bags of food offerings from the Rhinostery, and deliver one bag to each of the Yagudo who stand by the altars of offerings in Giddeus. Don't forget to report back to the Rhinostery after completing the mission.