There are a total of 4 Moonstones in the game and you must collect all of them to obtain this trophy. You don't necessarily need to have all four of them in your inventory at once, simply having collected all four is enough to obtain this trophy.
The locations of all four Moonstones are as follows:
In the very beginning of the game during the sword duel mini-game during the performance of I Want To Be Your Canary, impress all 100 nobles. See A Round of Applause for more information on the sword duel mini-game. Afterwards, when you control Steiner, head upstairs to where Queen Brahne was watching the performance and speak with her and she will give Steiner the first Moonstone. *Important Note*: This is the only opportunity to get the first moonstone once Steiner climbs the tower and the cutscene plays when he chases the princess and Zidane it is no longer possible to get it.
In the Conde Petie Mountain Path, there are four coloured stones you can find - the Red Stone, Blue Stone, Green Stone and Yellow Stone. Once you've located all four, place all of them in the statue in the screen to the right of Suzuna and Stiltzkin and you will obtain the second Moonstone.
Giving an Emerald to the friendly Jabberwock will reward you with the third moonstone. See Mister Nice Guy for more information about friendly enemies.
A fourth Moonstone can be purchased from Stiltzkin in the Alexandria Steeple after the events in Terra. See Driving the Hard Bargain for more information on Stiltzkin.
Once you've obtained your fourth and final Moonstone, you will obtain this trophy.