One of the easiest methods of killing the Destroyer is to use the Daedalus Stormbow. This item has a 20% chance to drop from Hallowed Mimics. Hallowed mimics can naturally spawn in the underground Hallow and in Hardmode worlds you can also use 15 Soul of Light to make a Key of Light and put the key in an empty chest which will cause it to become a mimic:
Hallowed, Corrupt, and Crimson Mimics can also be summoned manually by the player, in Hardmode worlds only, by placing a Key of Light or a Key of Night inside an otherwise empty Chest; the Chest becomes a Mimic once it is closed
The reason this weapon is so strong against the Destroyer is because it has a high rate of fire and also produces several projectiles for the cost of one ammo. Because the Destroyer is so long, it's nearly impossible to miss unless it's underground. The best ammo to use with the Stormbow is Holy Arrows, since each hit will spawn additional star projectiles for added damage.
As for strategy, I usually set up a very simple arena shaped like a flat U. I make sure it's floating about 50-100 blocks above the ground.
* * * = Solid block
* * C = Campfire
* * H = Heart Lantern
* C *
************ (Actual width should probably be around 30 blocks)
This shape prevents lasers from the main body from hitting you, which makes you effectively immune to the Destroyer itself (unless it approaches at an almost vertical angle and manages to jump straight up to the arena, which shouldn't happen often). The only thing you have to worry about are the drones - since they can travel through blocks and often end up above you, they will start shooting down towards you. This is why the arena should not have a ceiling - you can use the Stormbow to clear out those pesky drones.
Using this setup, with the right ammo and potions/buffs, possibly combined with other suggestions here (Nimbus Rod helps a ton as well), it's pretty trivial to kill the Destroyer in 30 seconds to a minute without much risk to yourself.