The bullet-sponge conundrum

One way in which game devs make bosses more difficult than the average enemy, especially in games trying to stay 'realistic', is by giving them huge amounts of health.  And this isn't inherently a problem.  You don't want a boss to kick the bucket as quickly as a grunt.
The problem some games face is that this is the only defining attribute of a boss.  In my whipping boy for this post, The Division, bosses are just named enemies that can eat more bullets, hit you harder, and drop shinier loot.  This leads to pretty uninteresting battles, since the boss has been made to take longer, rather than made to be more challenging.  Fortunately, I know a few ways they can fix this issue.

Battle damage

In Monster Hunter, when enough damage is done to a certain part of the monster, that part can be broken, or even completely severed from the body.  As well as providing a visual indication that you're hurting it, it affects the monster's ability to fight.  On the Barioth (a fearsome beastie) damaging the claws causes it to lose its grip on the ice, giving you crucial extra time between its attacks, and severing its tail reduces the range of its tail swipe attack.  This system rewards for actions throughout the fight, rather than just for finishing it.  In The Division, this could be done by giving the bosses destructible heavy duty body armour, and nerfing their accuracy and movement speed when you damage their arms and legs.

External objectives

A boss fight needn't be spent only fighting the boss.  The monotony can be disturbed by fulfilling other objectives, such as cutting the power to bring down the boss's impenetrable shield, or breaking into an armoury to acquire extra firepower.  This breaks the fight up a bit, and holds your attention since you know you're not just going to be doing the same thing from start to finish.  In The Division, this could be applied through optional objectives such as acquiring explosives and demolishing a wall to allow flanking, or grabbing flashbangs to stun them for a bit.

Behavior and attack variety

In Monster Hunter, (guess what my favourite series is), monsters can become tired or enraged for a short time.  When tired, a monster may lose the ability to breathe fire, or fall over when charging at you.  When enraged, they move faster, and use new attacks.  This makes it feel almost like a series of smaller fights, or a different form of a boss.  And having a wide variety of attacks keeps you on your toes, since you need to keep an eye out for telegraphs, and position yourself so that you'll be prepared for whatever they throw at you next.  Obviously an enemy that's shooting at you can't do this in the same way as an enemy with teeth and talons.  But they could change weapons periodically, such as switching to a shotgun and bearing down upon you, forcing you to back away before you get shredded, or whipping out a marksman's rifle and backing away, forcing you to press forward to maintain accuracy.

These are just a few ways a boss battle can be made interesting in a 'realistic' setting, and it's a little disappointing that The Division took the lazy route.  Then again, it's Ubisoft, so let's just be grateful the bosses weren't all just quick time events.