This Trophy is relatively simple and can be done in recruit.
In order to complete the requirements, you must play EVERY SINGLE MISSION without dying or reloading a check point. If you die at any point, or achieve a fail state for any mission, you must restart the mission from the very beginning. The easiest way is to press start and "RESTART MISSION".
You do not have to start a new game. You can get this by simply going to mission select and doing the mission of your choice. There is no tracker for this Trophy, so I suggest you keep track of what mission you have completed on your own.
Trophy will pop when the last mission under these constraints is completed.
Take your time and the joy the campaign on easy!