So what are some of the various challenges that you have heard of? I have only heard of the 3:

1. Low Level Challenge - never gain a level
2. Level Reks to 99 - self explanatory
3. Vaan only - never use more than Vaan in your party, all others to stay at lowest level. Only exception is the couple of times when you are required to have another character out, but even then they can't gain a level.

Any more that I haven't heard other than the obvious perfect game achieve everything one?