As long as there is an existing waterproofing layer, then an additional one doesn't need to be installed before re-tiling.
You will need to check for any drummy tiles by tapping on them with the handle of a screwdriver. If any tiles sound hollow, you must remove them and then re-glue them down.
Next, check for any high spots and grind them down. Once you have cleaned the floor and walls well, apply a primer to the surface of the existing tiles. This will allow the new tile adhesive to bond well with the old tiles. After the primer dries, you are ready to tile.
When removing tiles from plasterboard walls, there is a high chance that you will damage the board in the process. Plasterboard is a relatively soft material and when the tile glue bonds with it, a piece can be ripped out when removing the tiles. The damaged board then needs to be replaced before tiling over, and this is an additional cost. If it is just one row of tiles, it would be easier than a whole wall and there will be potentially less damage caused to the plasterboard. However, you might still need to replace the section behind them.
I have stripped back a bathroom's worth of tiles and it was neither a fun nor an easy job. However the tiles were set into a thick mortar on top of brick. I imagine tiles over Gyprock would be a bit easier to remove, and while re-Gyprocking adds another layer to the job it would be achievable if you are looking to keep the same dimensions inside the shower.
One concern I would have for tiling over the top of your current tiles is whether the plumbing fixtures will end up too far recessed and therefore unable to be removed/fixed if need be. Otherwise that seems like the quicker, more straightforward option.
Painting over existing tiles is also an option, and I have actually recently painted over the tiles in my own bathroom to a pretty good effect. I wouldn't go as far as to say that it is a substitute for retiling, but if you follow the directions carefully - especially regarding preparation - you can achieve a pretty impressive transformation for a fraction of the cost and effort. - tom_builds
I'm throwing my recommendation towards removing tiles and replastering the bathroom. I suggest removing the tiles including the plasterboard that it is glued onto. This will make for a quick demolition and totally avoid having to repair any plasterboards.
Here are some advantages of removing the tiles with the plasterboard:
It's the perfect chance to inspect your inwall plumbing fittings for leaks.
Now is the perfect time to update your shower set while the plasterboard is off.
There's no need to move any of your plumbing fittings.