Re: How to beat the big dude.
First off evaluate your situation: you don't always need to try to get the bucket yourself. I actually prefer forcing the defender to commit to allow a teammate (who should be filling in behind you) to have a wide open look.
Secondly practice spinning it off of the board from various angles. Since you are in control of the ball the defender has to guess at what you're going to do. Unless their Bismack Biyombo and can jump well after the show to swat it this is to your advantage. So knowing how to hit from various angles is key.
Thirdly I would recommend practicing space clearing moves. Many mentioned the euro step. I'm terrible at it so I have perfected the ability to jump stop to a position where the ball is protected from the defender. My favorite thing to do actually is to do a reverse layup so the rim protects me, so even if I'm straight on I can hop step at the basket so I'm positioned to reverse it.
And finally you need a shot of some sort. A tear drop, a pull up, a floater, a quick scoop, something so that the defender knows they can't just give you that. Then you can try to force them to commit and it opens up a bunch more options to hesitate, or spin off, or something.
Generally the bigs are slower, and honestly, I personally think the most uncomfortable place to be as a defender on a fast break is just sitting in the post waiting for the handler to bear down on me. So I would be that the defender is on their heels anyway. Just be confident when you go up, you'll likely get a positive result.