One way is to guard your sense doors, an example of this is that you are doing walking meditation and you are very mindful, you are just with your feet. Your mind goes wandering, you note it and come back, it wanders again, you note it and come back. You continue in this way and 40 minutes later you are done. You are with yourself the whole time.
Compare that walking to another time; you are walking along and you are start thinking, "Wonder what she thinks of me?" Then you are walking some more and you think, "She is looking at me, I know she is looking at me." And, you get these thoughts going on and on, and all the time you are wondering and worrying about other people's judgements and opinions. What's the basic reason? You are not being mindful of what you are doing.
The first walking that I mention, you are just mindful, you are just aware that your mind wanders and you note it and come back. You have no Dukkha worrying about other people's judgements and opinions. It's often that simple. In the second example there is a lot of Dukkha because you are feeding the thought, it's because you are getting continually distracted from what you are doing that you then have a problem. So, to be more independent from other people's judgements and opinions, be more mindful, guard your sense doors.
That's okay when they are not speaking with you. But what about when they are telling you off? They are giving you their opinions right to your face and you've got to take it. How can you be independent of that?
Deflect on Kamma, reflect that we are each the owner of our own Kamma. What happens if somebody blames you, what if somebody praises you? Is your happiness going to depend on what other people think of you? Let's say you do something that's very bad. And somebody blames you. That's okay, you can take the blame. Fine. Now what if you do something very bad and somebody praises you, actually thinks it was good. Does that change the fact that you did something bad. No!
Now what if you do something very, very good and somebody praises you. That's fine, that's fair. What if you do something very, very good and somebody blames you. Does that change the fact that you did something very, very good? No. So really, what you have to know inside yourself is what are you doing and is it wise, is it not, is it proper or not, beneficial or not. You have to decide within yourself.
In this way you become more independent from other people's judgements and opinions because you are judging yourself all the time. You are being more mindful and aware of what you are doing all the time so that other people's opinions can never ever change your own Kamma, never ever change what you have done.