How to Complete A Lady's Persistence
The objective is to weaken the Nagaraja, NOT to KO it. If you do KO it, you will fail the quest. You just need to bring the Nagaraja's HP down until it is HP Critical. You also need to make sure that Syrenead does not get KOed.
The law forbids Harming the Weak, but if you have leveled up your clan a lot, you might have no choice but to break this law. Units of the same or higher level than the wyrm will break the law if they attack it.
The terrain here makes it difficult to reach the wyrm at the top of the mountain, so you might want to bring Gria since they can fly and Dragoons since they have a high Jump stat, and you might want to use magic attacks since they are not restricted by the elevation of the battlefield.