You're a dance teacher. You criticized one of your students' dance technique, and now she seems upset and angry at you. You know that dancers get criticized a lot, so she needs to get used to it. You give her this advice.
You've got to grow a thicker skin if you want to make it in this business.
"You've got to" is similar to "you need to". They're basically the same in meaning. However, "you've got to" is more common when talking about general qualities that you need in order to achieve a certain goal. For example:
You've got to be both talented and persistent to make it as an actor.
"You need to" is more common when you're actually telling the listener what they should do, right now.
You need to go talk to Mrs. Green about that.
You need to stop spending so much on entertainment and put some of that money toward your savings.
"Having a thick skin" is an idiom which means not getting upset when people criticize you.
The phrase that means to become more unconcerned by people's criticisms is "grow a thick skin".
This is a neutral expression — not too formal and not too casual.
To "make it" means to become successful. For example, you can ask someone who's really successful this:
When did you first start to feel like, "Yeah, I made it?"
In some very competitive industries, like entertainment and the arts, people sometimes talk about "making it in this business":
It's hard to make it in this business.
When you talk about "this business" in a phrase like this, it means the industry that you work in.
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