Il ne fait pas du tout. -- (lit.) He doesn't do at all. This doesn't sound right. You are negating the verb "faire" without an object, so we don't know what he isn't doing.
Il ne fait rien. -- He doesn't do anything. "Rien" is the part of the negation and also functions as the direct object ("nothing"). This is what you're looking for.
If you want to be even more emphatic, you could say:
Il ne fait rien du tout. -- He doesn't do anything at all. But, in any case, you need "rien".