The Crescent Moon amulet is a unique item in Diablo 2: Resurrected and therefore drops randomly. You can’t be sure of finding it at any particular place or any particular time. But you can increase your chances of finding a Crescent Moon amulet by playing through the sections of the game in which it is most likely to drop.
Generally speaking, you’re most likely to get a Crescent Moon amulet towards the end of the game on Nightmare difficulty, or towards the beginning of the game on Hell difficulty. The monster with the single highest probability of dropping a Crescent Moon amulet is Andariel on Hell difficulty, with Mephisto on Nightmare, Diablo on Nightmare, and Baal on Normal not far behind. Baal and Nihlathak are the only Bosses that might drop a Crescent Moon amulet on Normal. Regular monsters won’t drop one on Normal at all. Even on Nightmare, a regular monster won’t drop one until Act V, and even then it’s highly unlikely. So, you’ve got a choice between grinding bosses, or the less repetitive option of playing through the first few Acts repeatedly on Hell difficulty.
If and when you manage to find a Crescent Moon amulet, then you’ll have an item very effective in stealing both Life and Mana, which is particularly useful when used in combination with the Sorceress’ Energy Shield skill.