“Under the sun” means on earth; in existence.

For example:

They discussed every topic under the sun during their long conversation.

I’ve tried everything under the sun to fix this lock, but I just can’t get it to work.

In this library, you can find books on just about every subject under the sun.

I looked everywhere under the sun for you! 

Where have you been?

Tradução:

“Under the sun” significa “na face da terra”, “no mundo”,

“em existência” ou “tudo que se pode imaginar”.