From P-XRD I can see the material has all the carbon phases in it. Probably the poly condensation phase involved in the synthesis has not been done properly ? Any suggestions in this regard.
I agree with the previous answer that more information is required. But separation of different carbon phases remain difficult, and is based on little differences of reactivity. For example, amorphous carbon more easily reacts with oxygen than crystalline forms, and is preferentially burnt at lower temperatures. But the other phases will be a little affected by such oxidation.
I agre with previos answers. Selective oxidation using different oxygen concentrations under controlled temperature conditions may be an answer. Also the use of other oxidants like water or carbon dioxide in the gas phase or even chemical oxidants such as nitric acid for example
TGA may be very useful in order to detect different phases and to check different conditions to selectively oxidise some phases and not others.