How is a shot like this done? (Smooth angle shift in extreme slow-motion)
I would have to agree with @Michael on this one, Bullet Time (as the name suggests when opening up the image "Surfing Bullet Time" would probably be the best result. To be fair it was probably filmed on a small boat (cameras in waterproof housings) as take just as the boat goes over the wave (just before it turns over) 

Here is the actual video


                
            

It was shot with 12 GoPro cameras