This is one of the most difficult trophies on all of PSN. You must complete all 320 of the game's levels. While the game is already very challenging up to level 318, the final two levels (319 and 320) are on an entirely different level. Here are video guides for levels 319 and 320:
It was almost a year before this trophy was earned for the first time. Its first achiever was Synophis, who earned it on July 22, 2014. Its second achiever was almost a year after that, on June 10, 2015.