Aristotle's eudaimonia sounds quite a lot like what the humanist psychologist Abraham Maslow calls self-actualization: achieving fulfilment by being all that you can be. One difference between is that the psychologist is trying to help us to be happy (which may involve leading "successful" lives), while I think the philosopher is trying to instruct us in how to lead a successful life (which may result in our being happy).
Another difference is the way that each provides supports his own thesis: Maslow identified a set of people who he believed were "self-actualizers", and then listed their characteristics, while Aristotle arrives at his conclusion by a process of logical argument.
It seems that Aristotle is saying that to be an excellent human being, we should behave in a rational way. We know what this should mean in any given situation, but it doesn't necessarily come easily or naturally to us. Eudaimonia is achieved by cultivating moral habits, so that it eventually becomes second nature, and we behave in accordance with reason without having to think about it.
I think that there are a couple of weaknesses in Aristotle's argument. First, if we accept that eudaimonia is the supreme good which cannot be improved upon, I don't think it necessarily follows that being an excellent human being provides that. For example, being a virtuous person doesn't guarantee you material comfort, or good reputation. Even if it does ensure an inner mental harmony, that cannot in itself be eudaimonia, because it could be made better by also having money and lots of friends.
Secondly, Aristotle says "ethical virtues do not come about by nature", and that we need to make a habit of acting in a way that will develop them. But it is not clear from this passage how we can know a virtuous choice is. Aristotle does say that we should make a choice "in the way a prudent man would determine it" - i.e. we should ask ourselves "what would a virtuous person do in this situation?" But this to me seems to beg the question "how do we know what a virtuous person would do?" Assuming such a person exists, then how do they come to know the answer?
Reference:
There is a very informative page about Maslow (part of a set of pages which are all worth reading, incidentally) at: