The Amulet of Annihilation can first be bought in Crustacia, where a Mad Monk sells one for 10,000 Jewels. The Monk will only appear if the player has no Amulets in their inventory, and can be encountered multiple times by getting rid of the Amulet in some manner.
Amulets can later be traded for in Nobilia Marketplace for 30 bags of Rice each. Refusing the trader's offer will get him to lower the price, eventually down to 3 Amulets for a single bag of Rice. However, haggling like this will have him refuse to do further business with the player.
Amulets of Annihilation can be used to book passage across the Desert of Doom with a skeletal boatman on either end of the desert. In Ivor Tower Alley, an armor trader requires an Amulet of Annihilation for each trade. An Amulet of Annihilation is also needed to trade for a Ticket for Exhibition.