When it comes to the question on why or how we get bored, one of the key factors that play into it is attention span. Mimus is a curious robot with a solid approach of the concept of simulating attention span. 

My idea of showcasing boredom would be to create a hobbyist robot - a creature interested in a lot of different fields, pursuing various hobbies such as knitting, cleaning or reading. While performing each of the actions diligently and very seriously at first, Bore will soon reach the end of its attention span and get bored of the task. The more time that passes, the sloppier Bore's actions become until it gives up on the hobby entirely to move onto the next one.