you could hire or buy a pressure-washer
it will take off loose, soft or damaged mortar, so do any patching afterwards.
apply your well-thinned mist coat on the clean wall, if it is still very dry and hungry I would apply a second thinned coat before your finish. Protect the top of the wall exposed to rain with an extra coat of two, having first repaired it very well to smooth surface that will throw rain off.
Your choice of white paint will of course show the dirt, especially near ground level where mud will splash up during rainfall. Some people like to put a black or other dark colour on the bottom foot or so.
If people reverse cars or other vehicles up to a white wall you will see round stains from the exhaust.