Lightning Returns: Final Fantasy XIII Death Safari is a Yusnaan side-quest that can be played at any hour, but only after you start The Legend Of The Savior main-quest.
Death Safari should be completed as soon as possible because you will receive four adornments for Candice (Adoring Adornments side-quest), and you will also be able to harvest Niblet Hairballs for other side-quests.
Furthermore, if you complete Death Safari, you will get the Death Game Ticket which can be used to activate a new side-quest in Yusnaan.
The following walkthrough refers strictly to the Death Safari side quest available in Yusnaan.
Description: “The suspicious gatekeeper, who once punched tickets for the Sneaking-in Special, is still at his post by the industrial area gate, but he is running a new event now. In Death Safar: A battle Against Ferocious Monsters! paying customers get to run around the industrial area slaying as many Niblets as they can. Sounds like fun.”
Requirements: Activate Main Quest 2-2: The Legend Of The Savior.
Rewards: 1200 Gil, Maximum HP + 80, Strength +8, Magic + 4, Dark Devil Ears, Dazzling Devil Ears, Pure Angel Ears, Cautious Devil Ears
To start Death Safari quest in Yusnaan, first you have to activate The Legend Of The Savior main-quest. Since there is no time requirement for Death Safari, you can trigger it any time after you start the second main-quest.
The client or the quest-giver is the Suspicious Gatekeeper you have encountered at 6 PM, while playing The Great Break-In.
His name is Wedge and you will find him standing at the entrance to the Industrial Area. Talk to him and you will be able to start Death Safari. Death Safari takes place inside the Industrial Area, and to complete it, you need 30 Niblet-Defeater Emblems.
Before entering the corridor behind Wedge, make sure that you have the Thundara spell equipped on one of your Schematas. When you are ready, enter through the gate behind Wedge and start killing Niblets. Each Niblet drops a Niblet-Defeater Emblem; which means that you must kill 30.
The creatures spawn randomly, so walk around the area, harvesting Niblet Defeater Emblems and Niblet Hairballs for the Trapped Canvas of Prayers quest.
Since the creatures also drop small amounts of EP, make sure you activate the Overclock ability while fighting large groups, and continuously cast Thundara on them. When you have 30 Niblet-Defeater Emblems, Wedge will tell you that you have completed the event.
Exit the Industrial Area, to claim you rewards. One of these rewards is the Death Game Ticket which allows you to enter a competition more difficult than Death Safari.
Finishing it is the objective of the Death Game side-quest.