Just unlocking the 20 red bricks is enough, you don't need to buy them for the trophy to unlock. The bricks are fairly easy to find, and if you are lazy, you can enter codes to unlock 19 of them. You can also enter the code for Red Brick Detector - 7AD7HE, and find the rest of the bricks on "easy mode".
The only brick for which there is no code is "Collect Ghost Studs". You'll find it in the Pendulum hall, the one with exits to the clock tower and the Owlery.