How does changing difficulties affect Absolution?

The last trophy I need for Hitman Absolution is the golden "Absolution" trophy, rewarded for completing the game on any Professional difficulty.

Difficulty's are divided in two groups:

• Enhanced
  • Easy
  • Normal
• Professional
  • Hard
  • Expert
  • Purist

I started on Normal difficulty for like 4 levels and switched to Hard because I was aware of the trophy. The trophy didn't pop after I completed the game (as expected).

My question is: Can I level select to do the missions I did on normal or do I need to start all over again?