In Pursuit checks who is closest with each shot. If you manage to fight him in a 2v1, alternate who is closer or have the person with the highest health stay in front to protect the person in back.
If Barik is hugging his Turrets, use fire bomb. The turrets cannot be moved once deployed, so he will likely abandon them if fire bomb lands on or near them.
Shock Pulse will bounce if it hits a deployable like Ying's Illusions or Barik's Turrets. If you are playing competitive and he is picked early, avoid using these two to make Shock Pulse more difficult to use.