Complete the game on XIII difficulty which is the hardest one.
However, there is also a trick to do this the easy way! Here is what you need to do:
1. Finish the game once on any difficulty you want.
2. Start a new game on XIII difficulty.
3. Skip the cut scenes until you gain control of your character.
4. Quit to main menu and go to Campaign/Mission Select.
5. Load the last mission and finish it. (There is no fighting scene in this chapter)
The game is really broken and completing the game on one difficulty does not unlock the achievements for completing the game on lower difficulties. So the game kinda force you to play the game three times to unlock all difficulty achievements. But with this method, you can finish the game once and unlock the achievements for all of the difficulties!
I take no credit for this method. I watched it on YouTube. Here is the video: