The
ugliest way? Polymorph Thax'sysilliya into a squirrel, then lead her into the "safety zone" (those big areas to the sides where
you can go, but the stone arches won't let
her go), and Dispel it. She is now trapped in a space too small to spread her wings, and they will eventually atrophy and become gangrenous. Send in Aerie (properly buffed, of course) to deliver the coup de'grace by whining the poor beast to death.