Map
Image provided courtesy of Vana'diel Atlas.
Strategy

The area where you fight Diabolos is 5 x 5 tiles.
When Diabolos gets to about 40% health, 8 of the 25 tiles will turn light blue for a split second before they dissapear completely.
If you are on one of these tiles, you will fall to the floor beneath, a room containing 6 IT Diremites; they won't hesitate to chomp you to death.
The above picture represents the tiles that fall. The same tiles will fall each time. Red represents the safe tiles, the light blue represents the falling tiles.
As you can see, it kinda looks like a skull.
The "D" on the map represents where the tanks and melees should fight Diabolos. Try to keep him pinned in the very northeast corner of the arena.
The "M" represents where the mages should stand. If you have the proper distance between these two markers, then the mages should be far enough out of range to avoid being slept and bio'd.