Can you determine if it is the outoing or incoming pipes that are rattling? Try flushing the toilet with the water supply to the tank turned off. Still there? If not, it's the incoming pipes making the noise. If it IS still there, then it's the OUTGOING pipes. If it is the incoming pipes, it would stand to reason that the problem is somewhere between the toilet itself and wherever the water pipes branch off to supply the toilet. This is assuming the sink/shower/ other fixtures in the same bathroom make no noise. If this is the case, the problem MAY be as simple as a new tank fill valve. If the valve is shutting off and on in rapid succession toward the end of the fill cycle this would create pressure and the lack thereof (also in rapid succession) and could possibly cause the banging sound. You can create an example of this scenario by holding the trigger of one of those "sink sprayers" only partially on where the water is kind of "stuck" between routing through the sprayer and the faucet.... Try manually raising / lowering the float (with the water supply turned on, of course) and see what happens. Anyway, that is at least a suggestion of how to do some "detective work" without demolishing your wall. Good luck!