If there were special objectives to complete... How would you want to find out about it?
For instance "Garuda"
SE could tell you how to do the wing incaps (What classes, skills and method) and tell you what affect it will have on the battle
or....
The could tell you nothing and see how many times people get owned before they realize (If they ever realize) that they need a Pug and Lancer working together to incap one wing.. and a Marauder and Archer to incap the other

There is also various middle ground.
1. SE could tell us there are special objectives but not tell us what they are or how to do them
2. They could tell us what the objectives are but still not how to do them
3. They could have clues in game, through quest dialogue help you ascertain what you need to do to make the fight easier
The less they tell the players about the strategy of the fight, the better. As it is, the primal fights are barely lasting a week (didn't moogle take a grand total of 2 days or something?) before the first LSes beat them and conceive a working strategy. I'm not asking for something as convoluted as Absolute Virtue, but still, they should leave us in the dark and let us figure it out.