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Use a tile drill bit to drill the tile. Switch off the hammer action :)
Depending on the depth of plasterboard you can get away with quite a bit because the tiles provide a lot of surface strength. Relatively simple wall plugs that are designed for plasterboard should work. My preference is Fischer. Once the screws are in place the shear strength is dealing with most of the weight unless someone grabs hold of it and pulls.
What are the recommendations for fixing a bathroom cabinet to a tiled, plasterboard wall.
It'll be fairly heavy once it's filled. Cheers