For this trophy you must clear the game in under 15 hours, this surprisingly isn't as difficult as it seems. If you've played the game previously, it may seem hard when you spent a lot of time exploring each areas, taking on optional tasks mid story and fighting through all heartless encounters. If one were to run straight through the game you can easily do it within 10-14 hours depending on the difficulty. For a straightforward walkthrough of the game, please refer to this GameFAQs Kingdom Hearts Final Mix Walkthrough.
Additonal Tips for Speedster
Skip all heartless encounters unless you are forced to fight them, don't worry about your level as boss fights and fighting forced fights in higher worlds will easily make up for it.
Keep in mind that you can skip either Atlantica or Halloween Town, of the two it might be best to skip Atlantica if you choose to do this.
The timer is moving at all times even when you pause with or with the xmb, if you have something you need to do simply save and pick it back up when you have the time to play.
Cutscenes don't add to your time but if you want to get this playthrough over with you have the option to press and skip it.
Once you have beaten the final boss meeting this criteria the trophy will unlock after the cutscene before the credits.