Don't fall for the myth that the path to success is catering to your boss's style and preferences.
Your boss's style and preferences may or may not be smart business practices. Your best path to success is to make sure you get clear and realistic expectations every step of the way, the necessary resources, fair and accurate and honest feedback, and appropriate recognition and rewards for your work.
It is true that you need to work out a regular routine for working with each boss. Not only that, but you'll need to align yourself as best you can with what "works" for each boss whenever you are working with that boss. Some bosses prefer updates in writing; others prefer verbal reports. Some bosses prefer big picture reports. Others like to keep track of the details. You should certainly try to tune-in to each boss's preferences. But you cannot afford to compromise on getting the basic elements you need in order to succeed.
If your boss prefers that you "take a stab" at a project without giving you clear expectations, then you had better probe a little. You need to find out: "So my concrete goal here is to see what preliminary "taking a stab" yields? And exactly how long do you want me to dedicate to "taking a stab"? And are there any things that I absolutely may not, should not, can not do while "taking a stab"?"
If your boss prefers that you "wing it" when it comes to the basic resources necessary to perform a task, you need to figure out what resources are necessary, where and how to get them, and whether you'll be able to get them in time to do the task. Or you'd better report up front that you'll be tackling the task without the necessary resources.
If your boss is not forthcoming with feedback on your performance, you need to find a way to monitor, measure and document your own performance. You need a way to track whether you are going in the right direction or the wrong direction, where course corrections and improvements are necessary, and how to continue building on your successes.
If your boss isn't giving you fair credit and rewards for your great performance, then realistically, how much longer are you going to be giving your great performance to THAT MANAGER? Why would you keep investing your limited resources of best efforts with a boss who doesn't reward you fairly?
The truth is, regardless of your boss's preferences and style, you need to make sure with every single assignment with every single boss that you get the key elements you need to succeed: clear and realistic expectations every step of the way, the necessary resources, fair and accurate and honest feedback, and appropriate recognition and rewards for your work. That's regardless of your boss's style and preferences.