Syd Highwind: Basics - Run in, tank and spank. He has a griffon the size of an aircraft that flies over the ring and drops a firebomb. Everyone except the tank needs to run out. The healers have to keep the tank alive, somehow. Then when the firebomb is over, you run back in and fight. Rinse and repeat.
Shadow/Interceptor: Basics - You start the fight like any other. Then Shadow runs off at about 400% run speed and kidnaps your tank with him. You have to figure out where he went and chase him down before he kills your tank. He does this several times. Plus there are creatures all over the island that will start attacking you as you run around. It's pretty funny.
Yes, they are named after FF characters. The third one is Strife McCloud.