Ocarina of Time
In Ocarina of Time, there are two ways to obtain the Big Quiver. Link can either win it in the Shooting Gallery of Kakariko Village with a perfect score, or in the Horseback Archery in Gerudo's Fortress when scoring at least 1,500 points. The Big Quiver allows Link to hold up to 40 arrows in total. If Link completes both mini-games, he will acquire the Biggest Quiver.
The Wind Waker
The Minish Cap
In Twilight Princess, the Big Quiver can be obtained by beating the first level of the STAR Game in the STAR Tent of Castle Town East Road in Castle Town. The owner, Purlo, will challenge Link to complete his mini-game in under 30 seconds. This time limit can only be matched if Link uses his Clawshot to easily track down all the orbs. After doing so, Purlo becomes shocked that someone has beaten his mini-game, and will then reward Link with the Big Quiver. As Link needs the Clawshot to do this mini-game, this cannot be done before getting it from the Lakebed Temple.
The Big Quiver holds up to 60 arrows at a time, double the original Quiver's capacity of 30. This extra capacity is great if Link ever finds the need to venture into the Cave of Ordeals, as arrows are very useful in taking out enemies from afar.