Best way to remove wall tiles without breaking?
 

I don't know of any way that you can remove and save the tiles
directly. However, since the plasterboard sounds shot, why not try to
take it down carefully with the tiles intact and remove the remains
from the tiles. A hacksaw blade should cut along the grout lines with
care.
Of course, you could always retile in a contrasting colour. That's
generally better than trying to match the existing.

John