I love to have Jyn in my smuggler list.

Jyn's ability Hair Trigger reads: At the start of a hostile figure's activation, you may interrupt to perform an attack that targets that figure. Limit once per round.

If Jyn is focused can she attack with three green dice?

Can Jyn use "Marksman"?

Can Jyn use "Tools for the job"?

I think that I can use red, green, green, green with "Marksman"...

Why wouldn't she?

She is smuggler so you play Tools for the Job on her. She is performing an attack, so you can play Marksman on her before declaring target.

If Jyn is focused , focused is used during the attack and discarded afterwards. Focused is mandatory.