Your best bet is to use your military experience to try to get an internship for a federal agency or private contractor. While I was not an intel analyst while I was in the Army, I still tailored my duties and skills that I had received in the military to what the specific duties of the position I was applying for. Most of the internships take place over the summer, and some are paid, but rare to get. You have to start somewhere and an internship during graduate school is what landed me many job offers.
Just to give you a little background about myself:
B.A. in Political Science (Cum Laude)
M.A. in International Security (3.98 GPA)
Internship with the Office of Naval Intelligence
The internship supplied me with a security clearance and job offer. While I didn't accept it, I have been receiving mulitple job offers since. Hope this helped.