Mirelurk Queens are just a tougher variant of normal Mirelurks so you can kill them using the same techniques.
It is important to realize that Mirelurks have a very tough exoskeleton. Shooting the shell of a Mirelurk does not do much damage, if any.
Aim all your weapons at their soft parts (mainly their head) and take cover to avoid their spit-attacks.
There is no difference in techniques you can use between any of the difficulty settings. The higher the difficulty settings, the more bullets it takes, but that is about it.
Use mines or good aiming (or VATS) to cripple legs so it is easier to get away from them. Use cover to avoid their range attack (and regain health, slowly).
Use buffs to help reduce damage they cause or inflict more damage yourself.
One weapon I personally found very usefull is the Spray n' Pray you can buy from a roaming vendor (I can't recall her name, but seems comes across as a bit of a dope addict).
It is a submachine gun which shoots .45 bullets which explode on impact causing 15 points area of effect damage. Its destructive powers are quite impressive.