Botherer will stop mid-air when it gets to ~43 PU away from an enemy tank, and will proceed to rapidly spray 30 projectiles that deal 5 damage each. At very close range, it does 1 damage per projectile, otherwise it does 5 per projectile.
Tormentor stops at the same range as Botherer and will fire 40 projectiles in rapid succession that each deal 4 damage. At very close range, it does 1 damage per projectile, otherwise it does 4 per projectile.
Punisher stops at the same range as Botherer and will rapidly fire 60 projectiles that each deal 3 damage. At very close range, it does 1 damage per projectile, otherwise it does 3 per projectile.
You can deal large amounts of damage with the botherer by moving close to the enemy, and shooting below them (into the ground) at full power. Only works if your enemy is higher than you. Video example appended.
If you must shoot Botherer and its upgrades at a range it is best landed if your opponent is near a bumper or if the angle it targets the enemy tank at gives a possibility of hitting enemy tanks behind your opponent.
If the arc of this weapon passes too close to an enemy, it will lock on to them which can ruin its potential damage.