Before you read:
I haven't read Kagan's book, this is just my interpretation based on the small quote in the OP's question.
So it seems that "what kind of person should I be?" is the same as "what should I do?" since the only way I can affect what kind of person I am is by doing things. And everything I do affects what kind of person I am in the future.
What am I misunderstanding about Kagan's claim that there are multiple possible focuses for answers to the question of how one should live?
To your doubts, Batman's got the answer
Here is my take on this. "Being" is an internal trait, while "doing" is completely external; it doesn't matter how mean or greedy a person "is", the world around them is only affected by what they "do".
Let me give an example:
A man could be outwardly kind and compassionate towards everyone, but inwardly only be doing it in self-interest, perhaps he has read some article somewhere that says that pretending to be kind is the best way to manipulate people. He goes to poor villages in African and helps build homes, but he doesn't really care about them, only goes so that he can sell them his new invention that allows them to filter dirty water. He helps a homeless man realize his potential as a movie actor (I'm just making up examples by the way) but then profits off him because he knows the homeless guy will be grateful and indebted to him for the rest of his life.
On the other hand, a person could be like Batman, who outwardly is a rich stuck up jerk who often profits in ways that hurt other people, and that is how everyone perceives him, but in reality, he is a crime-fighting vigilante that truly cares about his city.
However, notice the difference between the Batman example and the first example. In the first, I contrasted between what a man thought (bad) and what he did (good). In the second (Batman) I contrasted between what he seemed to do (rich jerk), and what he ACTUALLY did (fight crime dressed like a bat).
Batman doesn't seem like a counterexample to the first example after all, does it? He still DOES GOOD, people just not know about it.
Let's give the extreme example of religious fanatics who commit acts of terrorism. They do evil, lots of it, and inwardly think what they are doing is with good purpose, which would make them "be" a good person...but no one would ever say they were...
Two more examples:
Economics in a capitalist world is often said to be "evil", as its based on a philosophy that people should primarily work for themselves and not for others. However, if so much social benefit has come from it (and argue as people might capitalism HAS proven itself to be the most effective economic and political system in the modern day) can we really say it is evil? This makes me think of the idea of the "Invisible Hand", as quoted from Wikipedia:
The invisible hand is a term used by Adam Smith to describe the
unintended social benefits of an individual's self-interested actions.
Finally, let's take religious members of society that participate in religious missions and charity work daily. In "The Brothers Karamazov", (THIS IS NOT MY BELIEF, JUST ANOTHER EXAMPLE) Ivan suggests that people are only kept in check because of their fear of God. We can apply this same logic to these hardworking members of society, saying they only work for others because of their fear of death. That is, they believe that by being good they will reach immortality, and therefore want to work for the social benefit of everyone else: solely because it benefits them as well. Inwardly, they may be thinking "Ugh, I freakin hate these disgusting street kids" and "I sure wish they would all just get malaria and die" (allthough I said upward that this wasn't my belief, I really HAVE heard people say those exact words), yet they go on church missions to build schools in Central America. Are these still good people?
To conclude, although there is a difference between who you are (inside) and what you do (how you affect the world), at the end of the day it doesn't really matter: it is only your actions that really determine whether what type of person you are.
To quote Batman:
"It's not who I'm underneath, but what I do that defines me"
Thanks for reading! Hope it was of use!