It is very easy achievement.
1 Successfully complete the game on normal or easy.
2 In the options change the difficulty level on hard.
3 Load latest auto-save and finish the game.
4 Start a new game on the hard difficulty level.
5 After the first save exit the game to the menu.
6 Load previous auto-save (the last save of the campaign) and finish the game.
7 Achievement "Extreme Conditions" unlocked.