As you progress through the seven chapters of Story mode you will find that the final levels of every chapter are locked with three keys. To unlock these levels you must also complete all of the chapters' side objectives, these are the objectives that appear on the top-right side of the screen on the 'Level Select' page.
Completing the chapter along with the side quests in one run through is almost impossible to do and you will need to go back to levels and play the side objectives. Replayng a level you have already beaten costs only a third of the stamina that is required to play it the first time which makes it easier to complete. Once you have beaten all the chapters's side objectives it will unlock and you will be rewarded with new weapon blueprints along with some weapon parts before you are taken to the next chapter.