1. Patricia never takes criticism personally. She accepts it and doesn’t feel hurt—it’s like water off a duck’s back.
2. When I told my husband that the storm had ripped off a large part of our roof, the news was like water off a duck’s back He said, “It could have been worse. ”

Similar to: roll with the punches; take (something) in stride. The expression suggests that something has no effect in the same way that water rolls off a duck’s back, not penetrating the bird’s feathers.