For those who have not completed games in the Xenoblade Chronicles series, this page contains spoilers regarding the plot. Discretion is advised.
Story Exclusive Enemies are special enemies in Xenoblade Chronicles. They are story related minor enemies that the party is either forced to fight, like a mini-boss, or apply assistance to or summoned by Bosses. As such, they are (usually) limited and only appear during story related events, they can only be defeated once per playthrough like for the Quest Exclusive Enemies.
Unlike Bosses, Story Exclusive Enemies have a normal target window frame when looking at them. However they are fought like Bosses, that is to say the battle arena is fenced by a green field barrier (if the arena is not physically limited), they do not usually drop Treasure Chest. Although some of them can respawn during the course of the related story event, they will not respawn once this story event is achieved (except Face Nemesis, she appears twice).
Eleven types of Story Exclusive Enemies are also Quest Exclusive Enemies, they are all Mechon involved in Story Quests, except the Kromars and Conflagrant Raxeal. The four Defensive Kromars must be slain in order to rescue the High Entia worker during Save the Worker in Eryth Sea. Conflagrant Raxeal is a Unique Monster involved during The Magma Rock in Valak Mountain. The Sentinel Mechon is encountered during Lift Battle in Galahad Fortress. The two Defensive Guard Units and two M94 Guard Units are related to Fiora's Conviction in Galahad Fortress, defeating them while defending Face Nemesis is required to complete this quest. The M88 Watchtower, M97 Commander and Offensive Scout must be defeated during Materials for a Bomb. The group of three summoned Energy Devices apply assistance to Yaldabaoth in Mechonis Core during Save Bionis.