How to shut down Xin Zhao as Shaco:
Early Game - Utilize your superior pathing ability with Q blink as well as your faster clear speeds to constantly steal his unattended camps. Xin has an extremely safe early clear, but not a particularly fast one. Also use your invisibility and superior movement speed to put constant pressure on lanes faster than Xin can follow.
Mid Game and Late Game - Look for potential picks, and constantly split push.
If both of you are even, you as the Shaco will likely not outduel Xin Zhao, but you do not need to. You have far better early game pressure than Xin Zhao due to the nature of your kit, and can snowball your lanes much earlier.
Shaco has a weak mid game, and you must avoid team fights while you build up your items. Split pushing is the name of the game, and Shaco is very good at getting out when the enemy comes for him. Watch your minion waves and kill whoever goes to farm them.
This tactic of looking for picks and split pushing will continue into the late game, though at this point, Shaco actually has really oppressive damage against squishies provided you are not too behind.
The enemy Xin Zhao will also be doing his best to find picks and split push. He WILL be more oppressive than you in the mid game, and can turtle quite well against your team in the late game because he'll have decent waveclear by then.
Your best bet to win against his team is to get your laners ahead in the early game. The rest is basic objective control and teamwork.