In the first stage, the Peacekeeper mainly alternates between two attacks. When she takes too much damage in a short amount of time she will teleport away; at the beginning she sustains a lot of damage before teleporting but as her health lowers she teleports more often. In the first phase it stays relatively still like when Queen Bee spawns bees. But instead of spawning bees the Peacekeeper spawns Drones in this phase, they do not come from her body instead spawning in droves from off screen. When in this phase she will slowly try to move away if the player gets too close, she will also make a loud buzzing sound and give off an amplified version of the particle effect for Adamantite gear.
The second attack phase for the first stage is basically the charge attack of the normal Queen Bee, however, she charges faster and more often. While she is charging the Drones which have been spawned will also fly at the player. The Peacekeeper gives off an the trail effect of cobalt and shadow armour when she is charging.
The Peacekeeper goes into stage two when when it reaches 16,000 . Its stats also change to 53 melee damage, 78 ranged damage, and 17 defense. In this stage the Peacekeeper will barrage the player with a few volleys of missiles; these missiles will home on the player and cannot be blocked with a weapon. When they hit the player or fly for 10 seconds they will explode in a radius slightly higher than a bombs. No Drones will spawn during this phase but the Peacekeeper will still use her charge attack.
Credit for this idea goes to zoomo.
His profile can be viewed here: http://www.terrariaonline.com/members/zoomo.71392/