To unlock the Crossy Road secret character NESSY, you have to be playing as a UK character (any character from the update, excluding LLAMA and #THEDRESS.) While playing, you have a chance to see NESSY swimming in a river. Just jump on NESSY and you will have unlocked it. See the video to the left for more details.
Click on the category "Secret Crossy Road" to learn how to unlock the other characters