Beating the arcade on max isn't the toughest trophy by any means, however it will take a few tries to get down. My pick, personally, was Superman. Using superman you've got the choice of using his Lasers (Back, Back Square) or his ground pound move (Down down, Circle) to keep the enemy at bay. Naturally you'll want to jump back at the start of each match in order to get some space between you and the enemies. Darkseid has a similar Laser Beam to Superman if you would like to use him instead, though he doesn't have the ground pound.
Naturally, this will be less of a hassle at one round and 30 second duration however if you think you'd like to play it safe with two rounds that is also an option.