Berserker Queen in XCOM 2 Alien Hunters is not to be taken lightly even if you think you are well-equipped to take her out. Although she is slow and sloppy, she can close in on your squad fairly quickly and put you down instantly.
She not only has a high HP pool and a panic attack, but also an AOE stun and disable. As appealing as it may appear to rain fire down at her from a distance, do not that she is capable of closing in the gap and once she does, it is game over.
XCOM 2 Alien Hunters Berserker Queen
The idea is to make sure that she is not accompanied by enemies during the encounter. Moreover, try to encounter her in an area where you can easily get rooftop and ravel advantages. You basically need to block her from climbing up and slowly whittle away her large HP pool.
Even if she manages to catch up to your squad stationed on a rooftop, you can always toss a grenade in order to demolish the roof, have her take a little fall damage, and continue with the process. Also it goes without saying if you manage to create some gap between her and your squad, the entire engagement will get a whole lot easier.
Stick to this strategy! Do not let her run away and you should be good to go! Lastly, do make sure to share your own tips and strategies on how to beat Berserker Queen in XCOM 2 Alien Hunters DLC in the comments section below!