This achievement can be obtained by playing through the level in story mode (does not work in free play) and following the steps below.
1 - Play till you reach the last save point in the level, it is just before the final big stair case section
2 - Pause and then exit the level (do not save and exit just exit)
3 - Once back in the overworld load the level again from the map and finish the level
Doing the above steps sets the timer back to 0:00 allowing you to have the full 15 minutes for the last 3-4 minutes of the mission.