Rotate around right vector

I am trying to make my character look like it’s diving. It is a duck, and I need it to look like it’s searching for fish like a duck does. I need to do this by rotating around the y-axis, and as long as I don’t rotate my duck that’s perfectly fine. However, if I rotate the duck, the rotation goes very weird and the duck shakes around the screen. I was thinking about trying to use the characters right vector, but I don’t know how to do this. Is there any way of doing this?