I really like those achievements and trophies that you can unlock for playing on a higher difficulty level.
It gives the game a higher replay value if you ask me. Because after you complete the story or tire of multiplayer, you can always go the extra mile with miscellaneous challenges that you may not have thought of before.
As for games with achievements based on difficulty, you have Halo 3, Halo 3: ODST, Bayonetta, Brutal Legend, Record of Agarest War (solely for getting EVERY SINGLE TITLE IN THE GAME. That one is a toughie.), and I'm counting stuff like Rock Band and Guitar Hero. They encourage you to play a lot and master the highest difficulties just for a handful of points.
That's all I can think of right now, too groggy for a thought process.