I could care less about (something)

"I could care less" means that you don't care about something at all. Use this phrase to talk about something that annoys you. For example:

I could care less what she has to say. I'm done with her!

To be honest, I could care less about sports.

"I could care less" is actually incorrect. The correct phrase is "I couldn't care less", meaning that it's impossible for you to care about something less than you already do. However, a lot of  people say "I could care less" as well. It's technically a mistake, but a lot of people make this mistake.

climb the social ladder

Imagine that society is a ladder. The people at the bottom of the ladder are poor. The people at the top are rich, powerful, and famous. 

So when a person works hard to get promotions at work, make more money, and impress people, you can say that they are "climbing the social ladder".

This phrase has negative associations. We think of someone who "climbs the social ladder" as being a little bit greedy, sneaky, and aggressive,

(sentence) or whatever

Put "...or whatever" at the end of a sentence to show that you're not talking about only one specific thing. For example:

She's always asking for money for gas or whatever.

This means that this person asks for money for many things, including for gas.

Another phrase with a similar meaning is "...or something":

He said to get him a hamburger or something.

The difference is that "...or whatever" is more negative. You use it when you're talking about something that you don't like or don't think is important.