Assuming you don't have more important targets, hold your ult for when Vivian uses hers. Tag her with a bit of damage, then ult. Be wary of supports being nearby, or if she's running the Scapegoat card, as either will likely shut down the kill
In a straight DPS fight, Vivian does more damage than Zhin. If you have Deflector Shield up, you're likely to win the 1v1. Be wary of his ultimate and Whirl, as both will ignore your shield and the latter can place him behind you.