Question about Killzone 3 on Elite?

So I beat Killzone 3 on easy to unlock elite mode (which I do on all games where the hardest mode has to be unlocked by beating the game). Now I went back to beat it on elite and I beat the first couple of chapters. I just went to "choose a chapter" or whatever it is called then I picked the first chapter so it displayed all of the sub-chapters and it says highest level complete is still easy even though I have passed all of the levels in the first two chapters ... hang on let me see what they are called ... I beat all of "A NEW BEGINNING" and "EVACUATION ORDERS" but they are showing up as only beat on easy. My question is do you have to beat these all in sequence? I played a chapter in between on easy for a friend, but it was at the end of a sub-chapter and I started back up right where I left off even though it was not from a save point. 25 minutes of my life wasted?? I will pick a best answer for advice. They have a good system of telling you what you have accomplished through each chapter(and subchapters within the chapter). When I played it on easy I re-picked chapters multiple times to get trophies that I missed and then would pick the latest chapter and I ended up with all of the tropthies. But there is really no "Completed the Game" trophy for easy. There is only trophies for completing chapters.

So there is the background. Question:

When beating Killzone 3 on elite (whatever the hardest mode is called) do you have to play through without interruption or can you, for example; beat the first chapter completely, start a new game play blah blah blah, come back and start from the very beginning of the second chapter and finish the game?

Sorry for the long question, but I figured typing this out wastes hours of less time than finishing the game and seeing if I get the trophy.