The fish problem- "Finding Dory"

Imagine a fish trying to get inside a truck to rescue her friends. However, there’s a net placed at a point where distance from the water’s surface from the net becomes the same as the distance which the fish had covered from the bottom of the sea to the water’s surface. Assuming that the movement of the fish can be modelled by a curve function, what’s the minimum distance that the fish has to cover to get pass the net? What will be the equation for modelling the fish’s movement?