To begin with, recall that virtue-based ethics is a theory of ethics that maintains that an action is to be evaluated based on how that action informs the aspects of the agent's character.
The character traits of an agent are seen as either morally good or bad. They are called virtues and vices, respectively. Traditionally, things such as patience, courage, generosity, and honesty are seen as virtues; and things such as impatience, cowardice, greed, and dishonesty are seen as vices.
Because of the emphasis on character, the kind of question you would ask yourself is different to the kind that you would ask if you were primarily concerned with evaluating actions.
One reason you might be worried about this ethical theory is that the focus on character seems to leave other people out of the picture. Aristotelian ethics in particular centers around your own self-fulfillment or flourishing.
By contrast, ethical theories that are based on evaluating actions focus more on the ethical impact we have on others. That's because determining a right action usually entails making sure it respects other people's rights (as in deontology) or brings about the most happiness for everyone (as in utilitarianism).
Another problem with basing an ethic around attaining virtues is that it isn’t very good at guiding action.
Perhaps you could start by doing some courageous acts, in the hope that they might rub off on you, so to speak. But even then, it isn’t clear what exactly you should be doing.
This seems even more difficult for virtues that don’t seem like the kind of things you can learn.
Let’s say you want to develop the virtue of compassion. Being compassionate is more like a feeling or emotion than it is a skill. If you see someone suffering, it seems like either you feel compassion for them or you don’t.
It isn’t clear how you could go about attaining this virtue. Because of this, virtue-based ethics isn’t very good at guiding action.
What’s more, it’s difficult to determine what counts as a virtue in the first place. For this reason, the virtue-based ethical theorist must come up with a way to determine virtues and vices. One way would be to try to avoid extremes in character traits by going for one that’s in between them.
The problem with this is that it isn’t always clear if you’ve hit upon the right balance.