You can simply achieve this with Gson.
package stackoverflow.questions.q18932252;
import java.lang.reflect.Type;
import java.util.*;
import com.google.gson.Gson;
import com.google.gson.reflect.TypeToken;
public class Q18932252 {
    public static void main(String[] args){
        String json = "[{\"b\" : {\"a\": \"Hello!\"}}, {\"b\" : {\"a\": \"Hi!\"}}, {\"b\" : {\"a\": \"Hello2!\"}}]";
        Type listOfA = new TypeToken<List<A>>() {}.getType();
        Gson g = new Gson();
        ArrayList<A> result = g.fromJson(json, listOfA);
        System.out.println(result);
    }
}
With this result (I have added standard toString methods):
[A [b=B [a=Hello!]], A [b=B [a=Hi!]], A [b=B [a=Hello2!]]]
Since you are asking about a JSON file, ie a text file that contains a JSON string, please make reference to How to create a Java String from the contents of a file question for loading a file into a string.