As raskerino mentioned, the NMSCIE challenge is among the most difficult and the most popular. Breaking it down into its component challenges can yield additional challenges of its own--it's possible, for example, to beat Emerald and Ruby while playing a No Materia game. Low level games and speed runs are also common challenge game approaches, although I disapprove of speed runs in general.

Really, there's no need to adhere to any preset challenge system; sometimes it's best to simply create your own conditions. You might try taking an NMSCIE component, for example, and also exclude Limit Breaks, or items, or non-elemental magic, or whatever else enhances the experience for you.