As Bhushan said, "broke" means having no money. "Beyond compare" means you can't compare it to anything else. It usually means something good, but in this case, the speaker is emphasizing having no money. It's like saying "I'm extremely broke."

It means the person has less money than anyone else. They are so broke (poor) they can't be compared with anyone else.

Broke means - out of money Beyond compare means - extremely good at something

I wouldn't just relate this to money because the word "broke" is in this expression. Although people tend to use the word "broke" to describe insufficient finances, this expression can be used to represent a variety of "hardships". Broken beyond repair can refer to someone feeling they are at "rock bottom" (experiencing such a hard time in their life, that it's difficult for them to imagine the possibility of things getting better). It can just as easily be applied to emotional distress.