1. to criticise someone strongly, often without good reason
I'm not having a go at you, don't be so sensitive.
I was angry because I figured she was just having a go at me for the sake of it.
I've had a long day, I'm exhausted and fed up and you have a go at me as soon as I walk in the door.
2. If you have a go at someone, you attack them physically
The police had to stop the crowd by having a go at him.