I've never heard of an honors degree, and the phrase "as done honors science" is meaningless.
Maybe something called an honors degree exists in other countries. In the US we say someone has graduated with honors or with high honors.
Sometimes we're more specific and say that someone graduated cum laude, magna cum laude, or summa cum laude. Those levels of recognition are written on the diploma and are part of the graduate's academic record.
I don't like 1. I would change 2 to say she graduated in science. In BrE at least, we rarely refer to the honours part of a degree- most people who graduate get an honours degree, so it is nothing special.