The Amarok is a Melee weapon that falls into the yoyo category, a unique set of weapons that can attack enemies at a range easily yet still are associated with the Melee Class. It is very powerful in early Hardmode and can be accessed as soon as Hardmode begins. It also inflicts Frostburn which is one of the more powerful debuffs in the game.
The Amarok drops from any enemy in any variant of the Snow Biome. This means the method of farming for it can be varied and it can be found in a variety of places. The biomes it can be dropped in include the Snow Biome, Corrupted Snow Biome, Crimson Snow Biome, Hallow Snow Biome, and all of their underground variants. Though it has a one in 300 chance of dropping, it's not very rare due to the amount of enemies that might drop it.
The simplest way to farm for the Amarok is to pick a Snow Biome and kill enemies in it. While it isn’t the fastest method it is one which is easily combined with farming other items. For example you can farm in the aboveground Snow Biome during a Blizzard to also kill Ice Golems for their Frost Cores and Frost Feather. You could also combine it with soul farming by doing it underground in the Corrupted/Crimson Snow Biomes or Hallowed Snow Biome.
However, if you just want the Amarok the best way to farm for it by far is to summon events which spawn lots of enemies. Summoning the King Slime is good as by the time of early Hardmode the fight is trivial and he will spawn a large number of slimes which can all drop the Amarok. You could also use the Goblin Army as most of the enemies are pre-Hardmode, like the King Slime, which makes fighting them very easy.
If you’re still looking to combine it with farming for other things try using the Pirate Invasion. It’s a slightly difficult event due to being accessed at the beginning of Hardmode, however that means it also has Hardmode loot. The Cutlass is a fast and powerful Melee sword, the Pirate Staff is a very good Summoner staff and the Coin Gun, while rare, can match even the Megashark in power. All of these drop from the Pirate Invasion on top of a large amount of money so it's an excellent choice if you want to combine your Amarok farming with anything while still having it be relatively fast.
Once it finally drops you’ll have your hands on the unique and powerful frozen yoyo. It has good base damage and 18 tiles of range but the thing that really makes it worth getting is the debuff it inflicts. Upon hitting an enemy, the Amarok has a two in three chance to inflict the enemy with the Frostburn debuff. This is a very powerful debuff, dealing eight damage per second for its entire duration. With the Amarok inflicting it for about two to five seconds, it can be seen as bonus damage ranging from 16 to 40, almost matching the yoyo’s base damage.
The Amarok is a very strong Melee yoyo which is dropped by any enemy in the Snow Biome after the Wall of Flesh has been defeated. Farming it is simple and rather quick and even faster when using the King Slime or an invasion. Due to the Amarok inflicting Frostburn, it is even more powerful than it seems as the damage over time debuff is one of the most damaging in the game.
Blizzards are the Snow Biome variant of the Rain event. When it's raining in any other biome, that means there’s a Blizzard in your snow biome and Ice Golems will spawn there.
Normally the Pirate Invasion is an entirely random event but there is an item you can find to summon it at will. Killing an enemy in the Ocean Biome has a small chance to drop the Pirate Map which can be used to summon a Pirate Invasion.
If your Snow Biome is too far from Spawn to get the Goblin/Pirate Invasion in it you’ll have to move it. It’s a bit of a chore but definitely doable. It takes 1500 Snow or Ice Blocks on screen to turn the area into a Snow Biome. It’ll take a lot of extra work so definitely factor that in to whether or not you go for the Amarok in this way.