To get this achievement you have to clear every level in the game on ALL difficulty settings - that's Easy, Normal, Hard, and Ace (which unlocks once you clear the game on Hard). Clearing the game on a higher difficulty setting does NOT count towards the easier ones. In order to maximize your MRP payouts and minimizing the time taken I recommend going about it in this order:
First playthrough - Hard, play normally
Second playthrough (you get an option to restart the story once you finish level 20) - Ace, play normally
Third playthrough - Normal (this is a good time to do a No-Damage run for one of the medals counting towards the Highest Achiever achievement)
Fourth playthrough - Easy (this is a good time to do a Machine Gun Only run for one of the medals counting towards the Highest Achiever achievement)
Because you get an MRP bonus when playing missions in the story mode (as opposed to the free mission mode) AND it is the only way to fulfill the requirements for some medals, I recommend you do full playthroughs for every difficulty level rather than clearing missions individually through free mission mode.