Guide:Queen Bee strategies

Potions
Bring at least 5 Healing Potions. Ironskin Potions will also reduce damage, making the fight much easier.

Armor
Crimson armor/Shadow armor or better. Meteor Armor will also suffice. If however you don't have access to it, put more work into arena preparation to compensate, or just hold off fighting the Queen Bee until you have something better.

Accessories
Cloud/Blizzard/Sandstorm in a Bottle, a Grappling Hook, and Rocket Boots/Spectre Boots are very helpful, although not entirely necessary.

Weapons
Get the best bow you can and craft as many arrows (Fire Arrows or Jester Arrows) as possible. Also consider bringing a sword weapon like the Blood Butcherer, Muramasa or any other large sized swords. It will help when attacking the minion bees. It is easier if you have a Bee Gun, although you must have defeated the Queen before to obtain it. Collecting fallen stars, and using a star cannon, would kill her in about 70 shots. This is fairly effective for she is not immune to knockback. A Space Gun and Meteor Armor would make quick work of the Queen Bee due to its high fire rate and piercing ability. A Boomstick will make dealing with minion bees easier as well.

Terrain Preparation
Prepare a fairly large area to fight in, as the Queen Bee is about as tall as you can jump. Have wooden platforms extending from one side of the hive to the next, so you can jump to evade its charge attacks. Have a small pool of honey below the platforms in case you need a regeneration buff, and cover all other sources with blocks or platforms, so they don't slow you down during battle. A campfire or a heart lamp would greatly reduce the need for potions, as well.

Summon Queen Bee
You can either destroy the Crystallized Larva (found within hives in the Underground Jungle) or craft an Abeemination to summon her. This only works on the jungle surface or the underground jungle. Any other location and she simply won't spawn, like most other bosses.

The Fight
The Queen Bee has 3 distinct attack patterns. 1. She will try to level height with you and charge at you from left-right or right-left three times. 2. She will hover near you and spawn small bee minions which will then attempt to attack you by contact damage. 3. She will behave like a normal hornet and fly around, shooting stingers which have a chance to poison you.

When she tries to ram you, maneuver by going up and down, using the platforms prepared prior to the battle, or, if you have access to it, use Rocket Boots or a Cloud in a Bottle and fly/double jump over her charge attack.

If she starts spawning bees at you, switch to a weapon that covers a lot of space, like a large sword or a Boomstick if you have one, and attack the Honeycomb-like area of the Queen Bee, where the Minion Bees spawn

If she starts shooting stingers at you, don't stop moving. It'll help you avoid the stingers and minimize damage. Treat this phase as if you were fighting a hornet

Videos

 * Yrimir's epic Queen bee fight on the first day wearing cactus armor!