"Taking the world by storm"

"Taking the world by storm"
 

How would I say that? I know that in Spanish, the literal translation wouldn't be correct.

Does anyone have an idea about any phrases that mean the same thing as this in Spanish? Thanks in advance!

Tomar al mundo por sorpresa.

¿Qué te parece cautivar a todo el mundo en el caso de fama? Si es algo de fuerza, quizás ¿tomar al mundo por asalto?

I have another idea that it could be the same idea that Chileno said before, but even so I will telling you.

Tomar el mundo por los pies.

Here with that phrase is more colloquial using the toes when you are taking the power of the main world.

I hope this idiom can help you.

Thank you all! These are great!

You're welcome.