having a informatics, IT or engineering degree sure helps a lot...

But I do know a psychologist that by having strong self taught c++ skills landed into AI programming for expert systems on an engineering company before and now for a game...

But, as always, what matters most is (i would place it on this order tough some may disagree):
1 Who you know (and what type of relationship you have with) ppl inside where you want to land
2 Your social skills, and particularly the ability to make ppl trust you (in the end it is all reduced to a mater of them having confidence in you).
3 What you actually have to show related to what you want to achieve (the reel in cg, an assortment of the code youve written before in programming)
4 The amount of experience in a similar position freelancing or in another company you can prove to have.
5 Your academic curriculum (which in most cases happens to be a prerrequisite for 3 and 4 but not necessarily true unless you want to be a medic, civil engineer/architect, accountant or lawyer )