To obtain the Big Game: Enn Shoox standard quest in Xenoblade Chronicles 3 Future Redeemed, interact with the request board in the Command Center of Colony 9. For this quest, you’ll need to defeat a rare Shoox nesting in a cave along the lake’s edge to the southwest of Colony 9.
Once you take it down, the Big Game: Enn Shoox quest will complete! As a reward, you’ll receive 1160 EXP and 2720 Gold.