Defeat all of the Isle of Thunder rare mobs listed below.
All of the rare mobs listed are accessible in any Stage of the Isle of Thunder except the following:
Additionally, there is one other rare mob on the Isle of Thunder who is not listed, Ra'sha. He does not require a specific Stage.
Note that even if you can get to the location where the rare mobs are supposed to spawn, if the Isle of Thunder is not in the right Stage, the rare mob will simply never spawn (and neither will any Trove of the Thunder King in that area).