To be difficult with someone.

"Suzie gave him a hard time for not showing up to her recital."
"Stop giving me a hard time. There was nothing I could do about it."
"If you don't finish your project, the manager is going to give you a hard time."

A: "My mom gave me a hard time for one bad grade on my report card."
B: "That's a tough situation. My parents never gave me a hard time for bad grades."

Other Common Sentences

"Albert is making it difficult for me."
"He's getting on my case about my comment."