Some items in Terraria drop only very rarely from certain enemies. It's a pain having to farm so many enemies to try to get these rare items. Is there any way to make them drop more often?
Material drops and unique item drops, among a number of other things, are affected by the player's Luck, though this mostly seems to apply only to non-Boss enemies. A positive Luck score can as much as double item drop rates, while a negative Luck score can almost halve them. Luck is affected by a wide variety of factors, most of which aren't communicated in the game.
Ladybugs and Town NPCs - Touching a ladybug that was released by a player gives a bonus, while killing a ladybug (including using one as fishing bait) gives a penalty. Killing Town NPCs affects the same variable, with the Guide giving a bonus and any other Town NPC besides the Clothier giving a penalty. Only the most recent event is used.
Torches - Certain types of Torches in the area (within about 42 tiles?) will affect a player's Luck. Generally speaking, biome-themed torches will give a bonus when in the correct biome and a penalty in the wrong biome, while regular torches will give a penalty in most non-Forest biomes. Most other torches don't affect Luck, and multiples of the same type of Torch don't stack.
Therefore, to maximize luck, players should try to use biome torches whenever possible, as well as avoid using said biome torches in the wrong biomes. If the player is out of said torches, they should aim to use Bone Torches or any torch not listed above (e.g. Ultrabright Torches, Gem Torches) to avoid bad luck. Above all, players should avoid using regular torches in the Snow biome as that reduces luck the most.
Luck Potions - Having the Lucky buff from a Luck Potion will increase your Luck score. Longer remaining durations on the buff provide a stronger increase.
Lantern Nights - The Lantern Night event occurs the evening after a boss or invasion is defeated for the first time, and provides an increase to the player's Luck score through the night, even underground.
Garden Gnomes - If a Gnome enemy is exposed to sunlight, it turns into a Garden Gnome, which is a piece of furniture that gives a Luck increase to players nearby (about the same range as Banners and Campfires).
These different factors all stack additively with each other.
In addition to this new Luck mechanic, the previous options for getting an item to drop sooner -- Expert Mode and increasing spawn rates -- still apply (see below).
(With one exception for some items. See below.)
Obviously, the faster enemies spawn, the more you can kill, so the more chances they have to drop the item you're after. The spawn rate of enemies can be increased in a few ways:
These effects do all stack with each other, but you can't stack multiple of the same item. So the highest spawn rate increase possible is by using a Battle Potion with a Water Candle placed nearby (during a Blood Moon, if applicable).
This is the only thing you can do to increase your chances of finding an item.
The only exception to this general rule is Expert Mode, which is only available in the Desktop, Console (PS4/Xbox One/Switch), and Mobile (iOS, Android) versions of the game. In an Expert Mode world, some rare enemy drops will have their drop chance increased, sometimes as much as doubling. Obviously, you need to create an Expert Mode world if you're not already using one, and Expert Mode comes with its own set of complications, so try it at your own risk. If you want to find whether your particular item has an increased drop rate in Expert Mode (and what the new drop rate is), look up the monster that drops it on the Terraria Wiki.