I have no idea how much time you have to prepare.
But first and foremost, I would say you need to prepare yourself to be OBSERVANT and LOGICAL.
Just think of how Sherlock Holmes did it...or how they do it in all those TV shows...and you should be fine.
A strong basis in medical and medico-legal backgrounds are important, but you need time to sit down and process and understand all that information.
I wish you luck in your competition.
------
As an aside, I'll give a sample forensics question (a simple one that came up in my orals)....
------
You are presented with a severely burned body.
History: Firemen were called to a burning warehouse where the body was found after putting out the fire.
Closer inspection of the contents of the warehouse indicates that it was used as storage for fireworks and firearms ammunition.
Inspection of the body shows a bullet wound.
(I could give you a location of the bullet wound, but it isn't relevant...that is why my examiner didn't give one to me).
Is this a case of an accident, a suicide, or a homicide?
Support your conclusion.
----
If you can figure this out, then you thinking on the right track and you should be able to do well.
----
(by the way, if you ever get to orals...they are TOUGH...not only do you have to think on your feet, you have to think quick...if you hesitate even for a second (Um...well...), the examiners would IMMEDIATELY move on and ask you another question)