This is a cumulative trophy that unlocks the same time as:
Simply beat the game on Hard mode or higher to get the trophy. To limit the amount of time spent on the game, it would be better to just play on this setting at least once. Worry more about the story and don't focus on the Arena until after you complete the game, and then drop the difficulty back down to Casual and finish off the other tournaments (Silver, Gold, Raritanium). It makes everything go by so much easier.