preparing bathroom wall for tiling
It is not uncommon to see tiles glued straight onto plaster or wallboard but it is not a good practice, IMO. Even if you were to pursue that method, you would have problems due to the glossy painted area (tiles won't stick) and the uneven areas (tiles won't lay flat).

I would recommend either taking down the entire wall surface and replacing it with tile backerboard (best), or scraping/sanding it as flat as possible and adding a layer of nice new flat backerboard (you could use the thinner 1/4" board in this case).

If this is an area that gets wet (shower/tub area), there are additional steps/considerations needed to ensure no future water damage.