You get into chaos mode by basically destroying any objects. The very first time you can achieve chaos mode is on the very first level.

This mission will begin and you have to enter an enemy base, whilst inside here you will need to find 5 memory cards. Follow the objective markers picking up the first memory card & killing any enemies you encounter until you get to the second memory card. This will be located right next to an AA gun. Pick up the card and enter the gun by pressing , this is where you can now get this trophy. An enemy plane will fly close by so just fire at that to take it down, next just fire at any objects you think can be destroyed, this may be buildings, boxes, radars, lampposts etc. When you see CHAOS come up on the screen in fiery letters you will get the trophy.