You'll need to earn a total of 10,000 casino coins to earn this trophy. Coins purchased with gil don't count towards that total.
In my opinion, the best way to do this is to go to the slot machines with a starting amount of 1,000 coins, get a rubber band set up on your L1 button, and let it go for a bit. Keep watching your screen in case the slots start falling into a pattern that yields nothing for you. If that happens, just hold down the left stick to keep the reels going and let it go when you want to stop a reel. That way, you can manually reset the pattern.
The goal is to get into Super Victory Mode and hit the 5,000 coins jackpot twice. It shouldn't be too hard. There's not a whole lot of rhyme or reason to how the slot machines work, but considering how fast you'll be going through turns, you can still finish quickly. In fact, it's very possible to get this trophy in less than an hour, even assuming that you start from nothing.