What should the grammar be in these two sentences?

"The lady’s slipper orchid attracts attention because it’s beautiful and rare. Yet this is its biggest downfall; it’s rare because it is so beautiful."

I would write it this way:

...rare, yet this...

Sentences have to be complete and they aren't supposed to start with conjunctions, i.e. but, however, therefore, yet...

Here's a good site for you.

https://www.skillsyouneed.com/write/punctuation1.html

Ok, thank you. But the semi-colon is correctly used?

Yes, perfectly correct, and you are more than welcome! Welcome to the English language I'd say you were doing pretty well.