One significant E.Skill to make sure that you ditch if you want a tiny difficulty boost is Big Guard. My first play-through of this game remained ignorant of it, and being in elementary school, the game was fun and I had some trouble in certain parts. Staying away from E.Skills entirely should boost the difficulty even further. Also, force yourself to attain the secret characters (Vincent and Yuffie) at the moment you are able to do so. The boss before getting Vincent is pretty difficult at that point of the game. And while getting Yuffie isn't much of a challenge, her side-quest in Wutai is some kind of ordeal if you're at a low enough level. It made me want to kill myself when I was younger and I was stuck in the middle of it.

Don't get Final Attack materia. Don't get Knights of the Round. Don't utilize any intelligent materia pairings. It's a real smurfing shame that the minute you begin to get intelligent with this game, you've pretty much gimped the whole challenge and the only thrill is invoked from watching your party perform more actions in one turn than they are supposed to.

I do believe there is a hack for the PC version of the game that makes it significantly harder, but I could be mistaken. Look around. I've never used it.