How do I win him back?

You don't need one more chance, you didn't mess up the last time dear! He just moved on, and you should too. All you can do is tell him exactly what you feel and move on, if he comes around it will be because he wanted to, and your relationship will be better than if you try to force it. How would you feel if a man tried to make you stay with him and you didn't love him? You have sincere feelings for him, I respect that! But you are also being selfish, and true love is not selfish. I know you are a better person than that, right?

You said you like your boyfriend but love your ex?

This is serious. But you see from his behaviour aren't you sure that he doesn't have the same feelings for you? And he's having a good relationship too so don't mess it. Try and get over it, I know it's gonna be difficult but if you like your boyfriend that much why don't you spend loads of time with him and not your ex?
For the beach thing, it's better if you act like friends and get over the love thing and if it is possible why don't you bring your boyfriend? That way you could be with him more and think about your ex less.

Now you are both in sepreate relationships and you as a good friend should respect him as well as his new girlfriend. He said he doesn't feel the same way about you anymore. BELIEVE HIM.
Now if you like your new boyfriend you should give him the respect he deserves as well. If you find that you can't, you may want to let him go before he finds himself in the middle of this and is hurt too. The best advice I could give anyone is to make sure you are over the last before you move on to the next. In order to avoid causing someone who is a good person to be hurt, due to your issues.
Now as for winning back your ex, you cannot make anyone love you and you cannot make anyone be with you. Try to keep that in mind when making your decision.