Hold L1 + R2 and rotate the Right Analog-stick clockwise ten times at the cryptographic sequencer. In this mode you will retain ALL your unlocked items and the challenges will be harder. When you have completed the main campain in Normal mode or above New Game Plus will become unlocked.
This mode will become available when you have beaten New Game Plus without dying once which means you must complete every mission and quest of the main campaign without making a single fatal error.