Painting or Staining Terrazzo Bathroom Floor

If you are talking about a terrazzo floor that is the true 1930+ polished/coloured and aggregate terrazzo, then it is actually only about 13mm thick and is integral with the rest of the next 80-90mm of concrete floor, taking it up will involve taking up all the concrete and going down BELOW the floor to the substrate (soil) if it is concrete slab on ground, or to some some form of suspended timber/fibro subfloor that the concrete ( about 100mm of it) has been laid on top of. Then you will have to waterproof it again to modern standards.

It is fine to tile over existing terrazzo, but that may well give you clearance problems as that will/may raise the floor by the thickness of the tile and adhesive that you use. A good tile adhesive and tile will last another 30 years - at least my parents floor did.

hope this helps