There are a few places that people deeply want to work at because of the type of work you will be able to do- getting into that bureaucracy is the only way to do it- (NASA, The United Nations, The World Bank) at these places you get work that unless you are a contractor (which is an entirely different maze). It may not be for you- but there are people that have studied and worked for years to "get in"- this advice is for them.
But the other rules still apply, and the best way into these entities is by taking the power of HR away and talking directly to people inside.
My experience (EBRD) was that it was possible to switch from temping (got that through a friend) to contracting to employee (I turned down the last). Friends at the World Bank used a variety of methods to join, but all benefited from talking to professionals inside along the way. These tips are important, but it's far better to have the HR person know that there is existing demand for the applicant.