Or can I just start tiling over the painted wall?
in a shower or bath enclosure you definetily NEED backerboard. If you are tiling other wall surfaces, as long as the paint isn't glossy, you could tile directly on the wall. thats also assuming whoever built your house did put up the correct moisture resistant drywall and not the cheaper drywall.
The short answer is you dont NEED backerboard. Before backerboard came into widespread use, tile went directly on wallboard. But, you'd be well advised to use backerboard. Tile used to fail in those old days. It is much less likely to fail today because tile setters routinely used backer board.
I would recommend using cement board in the shower (assuming you will be taking the green board out). You'll be using the 1/2 cement board for the walls. While you're at it, don't forget to install a moisture barrier, and be sure to seal the joints of the cement board with modified thinset and waterproofing membrane, and don't make the mistake of using mastic for setting tiles. If it's just around the bathroom walls and not in the shower, consider the size and weight of the tiles. If they are just your standard 4 1/4 tiles, just tile straight to the wall. Make sure the surface is prepped properly. Shoot me an email if you have any other questions.
I can't believe I, as the lone female answering, am going to have the right answer. Yes, you need backerboard. Simply put, you are tiling. Have you ever lifted a box of those tiles? And can you imagine one of them on that wall? Now, how about 10 of those boxes? You see, you are putting up tile and tile cement and tile group, all very heavy items, onto what may well be simple sheetrock. Yes, you need backerboard. Specifically, you want cement board, which is specifically designed to be used with tile and be waterproof. You see, in your zest to prove you can do it, you may well have a moisture issue come from an overlooked mistake in the tiling. Maybe it's the caulk at the tub seal, maybe it's in a corner, maybe it comes from an awkward merging of two tiles. Whichever it may be, you want a waterproof surface which will stay intact from such an issue ... sheetrock, no matter how nicely painted prior, simply won't do that. Yes, you need cement board. Ask anybody at your local home center if you doubt me ... and I, as the lone female, will now bid adieu.
No, you don't NEED backerboard BUT, I'll tell you from experience that it's much easier to work with, makes a better bond and you will have less trouble later on. I recommend the stuff with the little squares etched in (Hardibacker). Good Luck.