I think all NMs should have a rage mode, complete with music change when their HP gets low. Maybe an aura or different animation during the mode too (or glowing eyes).
Think of it like this:
Normal battle: http://www.youtube.com/watch?v=L4FpT...eature=related
Desperation mode: http://www.youtube.com/watch?v=CxA5ElDNqUA
Really brings out the feeling that you have to hurry and put and end to the fight. ( I know those themes are from FF 4 Heroes of light, but those best convey what feeling i'd like them to evoke).
Another good example is the way dynamic music is handled in Skies of Arcadia, or even the recent Pokemon Black/White version games.
This would serve to not only increase the challenge of facing a boss or notorious monster for parties, but would also increase the amount of strategy or tactics needed before taking down the enemy. You would have to plan for whatever increased danger, whether an invulnerability to physical/magical attacks, increased evasion, increased counter attacks, or a totally different move set, and utilize various abilities to win the battle.