When trying to change the difficulty during a game a warning is shown that "some achievements will not be unlocked". Which achievements are affected by a difficulty change?
The only affected achievement is Legend, which requires beating the game on Give Me Deus Ex difficulty (hardest). If you want to get that achievement, you must start a game on Give Me Deus Ex difficulty and never change it.
PS: I encourage playing on Give me Deus Ex difficulty. That is the way the game was meant to be played.