You can try it out with online classes on robotic engineering at Udacity and complete a certification. This would be less costly.
In my experience, robotics is a very vast field which could encompass many other subjects like electronics, electrical, computers /programming & mechanical engineering. At a minimum, bachelor of science (BS) degree would be the one to go for. There are universities that now confer BS in robotics.
I recently toured robotics labs at Georgia Tech as part of National Robotics Week, and we had the opportunity to learn about how students in a variety of degree programs were working with robots including physics and mechanical engineering.
You can learn more about the event and the robots here--> http://robotics.gatech.edu/outreach/NRW