I just helped my girlfriend and a friend on the Shiva server do this mission. We set the record (2 minutes, 50 seconds.) We came with a naked elvaan BLM. (I hear the screams already..) An eva build MNK, Great Sword sporting WAR and a NIN with no DD gear. We buffed in the field. The BLM landed sleep and then started healing. I (The ninja) tanked to start. The Monk used Hundred Fists and nearly soloed the eye. The warrior's mighty strikes hit the dragon until it was about 40% health.
The BLM healed me, (The Ninja) to full health and I popped Mijin Gakure. 350+ damage and killed.
For all new rank up-ers. Don't worry about getting a healer or Paladin. I would say sleep is unecessary, due to how quickly the eye fell. Grab 3 good DDs with standard exp gear. Have them two hour and the rest is cake.