You get this trophy near the end of chapter 3 inside seventh heaven, while you are waiting for Tifa and the gang to finish their meeting. The Dartboard is located to the left of the door.
All you have to do is get a score of 301 in 7 or fewer shots, 8 shots will tie you in first but will not unlock the trophy. The quickest way to unlock this is to aim for 5 triple 20s which will equal 300 and 1 single 1s which will take you up to 301.
The aim is all over the place so the best thing to do is move the thumbstick slowly when aiming, wait until the aim reticle is in the yellow crosshairs - you will get two chances to throw the dart, so take it slow and don't rush it.
Video guide: