There are four variations of Jay to unlock, you do not need to buy them for this trophy.
Jay is unlocked by beating level 4, Ninjacopter.
Jay ZX is unlocked by beating level 19, Min-droid's return.
Jay Teacher is unlocked by beating level 21, Ninja Crush.
Jay Gold is unlocked by beating level 28, System Override.
So you don't need anything extra to get this trophy, just complete story levels. The trophy will pop after completing level 28.