Has the bird been showing signs of illness (wheezing, nasal discharge, abnormal droppings, sleeping more than usual etc...), or does it act healthy with just bad looking plumage?
To me, the bird looks unclean, like it has not been bathed in a long time. Parrots need to be misted with water, enough to thoroughly soak the feathers, at least once a week. The owner should buy a new spray bottle (NEVER use one that has had anything but water in it) and spritz the bird with it on the mist (not the hard spray) setting with baby bath temperature water (warm but not hot), then let the bird dry off in a warm room (so it will not catch a chill).
Second, how old is the bird and what is it's diet? Poor diet can also cause poor plumage. If it is eating nothing but seed mix, it needs to be converted to a fortified pellet diet supplemented by fresh fruit and vegetables. If a parrot has been on a poor diet, it can take a long time to see improvement in the plumage as it takes time for them to molt out malnourished feathers and re-grow healthy ones.
Third, how big of a cage is the bird in? Does it have ample room to raise it's crest without brushing it on the top of the cage? Small cages can also cause feather damage as the bird struggles to move around comfortably, or in the case of cockatoos, if there is not enough room above them to raise their crest brushing it along the cage bars can damage the crest feathers.
Lastly, I know leg shackles are still popular in some parts of the world, but they are dangerous and can cause serious injury or amputation/death. The owner needs to buy a body harness for the bird, which is much safer.