There was a video posted on the Main Forum a while ago of a Monk doing the battle solo, so it IS possible, depending on your job, etc. The monk in the video used several very expensive potions, etc to ensure that he survived, and used his two-hour, of course.
I don't think this is a battle that most people would want to try solo. It can be a little tough. You don't really need a full party of level 25 either though. The main things you need are a RDM or BLM to cast Sleep on the dragon so the party can focus on the Eye, some sort of healer, and someone to tank and deal damage. I've done this in a party of 4 at level 25 (SAM, DRG, BLM, WHM), and had no trouble winning. Just be sure to sleep the dragon, and kill the eye first. Things can get a little chaotic if you try to fight both enemies at the same time.
With a full party of 6 level 25's, it's a joke.