This is my first time doing this so if its too vague or not good please let me know.
Ive read numerous boards indicating that in order for this trophy to pop correctly, starting a game, then switching to hard will not work. What needs to be done is switch the game to hard, save, start a new game then it will automatically be on hard mode...
however...
When I first started the game I went to options then switched difficulty to hard. Played through the game and beat the game today. Fought the boss, let the credits roll, watched the after credits movie, ( i didnt push any buttons btw) then it brought me back to Empire City with the "congratulations" message indicating that i can finish side missions, get some extra trophies etc. After I pushed the X button to continue about 5 seconds later the Hard Finish trophy popped up. So just to let everyone know that it does work this way.
Hope this helps.