You only need to purchase all of the items for Bahamut and Krystal. You purchase items with CP or Corp Points that are earned in game. The DLC character's don't count towards this trophy. In order to fully obtain all of their items, you need to accumulate a total of 225,550,000 CP for each character. You have to play as the character to earn CP for the character.
You can grind points on the 2nd Stage: Jungle. When you reach the sub-boss with the alligators on either side you can grind out points here. It makes life a lot easier if you find and keep the flame power up. It has the letter "H" on it. Note that eventually the combo will max out and your points will no longer count. You can either continue on and finish the stage or kill yourself and get a game over.
Corp Points will save any time you get a game over or complete a stage.
See video for the location of the grind spot (credit to Treasurefan02):