There is absolutely no way to kill the queen before she gets through the wall it's not possible without a way to either extend the time or freeze her in place.
The ballistas do not do enough damage and only take small segments of her health out on top of that take forever to reload.

I shot her directly in the mouth and it did no damage which is complete crap because anything that takes a direct shot to the mouth (Especially an explosive) will take massive amounts of damage.

On top of all that, after getting her so low on health, she stops taking damage no matter where I hit her.