Actually, Augustus did not embellish his accomplishments. He was keenly aware of the reasons behind the assassination of Julius Caesar, his Uncle, and was determined that he would not suffer the same fate. There is some argument that he wanted to restore the old Roman Republic, but events had moved Rome too far away from that goal. For that reason, he tended to downplay his role as Emperor. He wore simple clothes and lived in a modest house, and referred to himself as Princeps Civitatus, or "first citizen." He often promoted himself simply as primus inter pares, or first among equals. He was awarded the title of Imperator(hence "Emperor") simply because he was head of the Roman Army and had won a great battle at Actium. He made no great changes in governmental structure, although he did acquire a great deal of power for himself. So, Augustus did the exact opposite of "tooting his own horn."
Yes and no.
Of course, any leader is going to embellish his accomplishments. We need look no farther than our own politics to see that. Anyone who arranges to have an account of his accomplishments engraved in bronze and set on the front of his tomb is not modest.
But this question seems to imply that Augustus was "tooting his own horn" excessively and that his real accomplishments were lacking. I do not believe that this is true. Augustus accomplished many hugely important things during his long reign. He brought stability to the empire which had been lacking. He did a great deal to improve the physical infrastructure of the city of Rome and of the empire. It is largely because of things he did (such as building roads and creating a well-organized army) that the Pax Romana came about.
So yes, Augustus did embellish what he did, but his actual accomplishments are enough to make him an extremely important figure in Roman history.