The Knockback Shield is the (only) essential piece here.
You want to get the queen to very low health, depending on the amount of damage your parry does this value changes accordingly.
Then try to kite her at the very edge of the arena as shown in the video; Grab onto the ledge then dodge roll back off it, double jump onto the wall and rinse and repeat until she stands on the very last tile of the floor.
Once her feet are on said tile, jump up into her, place yourself slightly to her left and see if she performs an attack from the right. If so, parry it with the knockback shield to knock her into the void.

Her placement and health have to be very specific, otherwise the achievement won't work; if she dies and THEN falls off, it doesn't count.
You can tell the achievement is complete when the final cutscene plays immediately after her death, rather than having to interact with her again.

If she dashes back to the left simply hug the ledge again and repeat until she gets in the right position.
It is also recommended to not have any effects such as freezing, poison, bleeding or burning on your shield to avoid her dying to those effects instead. I've had that happen several times, it is unbelievably annoying.