Add stuff to the scene that's not just damage. Stuff that splits their attention and requires some strategic thinking.
- Mooks are doing a ritual that will have bad results if it's completed in two rounds.
- Mooks flee to sound the alarm/get reinforcements
- innocent hostages are at risk
- some of them are fake hostages and will attack if "rescued"
- some of them are actually innocent, but are dominated/acting against their will
- any number of gimmicks that force people into smaller groups.
- the boss is tangible only to one player at a time. Like that time in bg2 when I cast time stop and everything stopped except my wizard, and the demogorgon.
- the boss is split into X parts that need to be killed at the same time , in separate rooms.
Also, playing Mage and Fate most recently it's been really refreshing not having any of these DND problems.
This, this, this.
Also I often find inspiration in mechanics from MMOs, RPGs, and boss fight games like Elden Ring.
- Shifting damage resistances based on HP phases or whoever crit it last
- Phases where the boss takes no damage and the players have to do individual actions around the room before N turns or the boss heals
- Forced side battles where one or more players need to kill a mook in another room before returning to battle
- Shields that go down when players step on specific pressure plates, ensuring they're in range of my dmg
- Capture the Flag style McGuffin delivery to kill the boss
- Boss is fleeing through a dungeon at ~1 room per 3 turns and the party has to complete room objectives to reopen doors/keep up with him/keep LoS.
- Boss has resistances to all damage until hit with N conditions when those resistances drop for N turns
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Use the maximum HP possible from the dice instead of the average given (eg. 6d12 = 72 instead of 39), or at least a higher portion of the maximum quantity
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Increase AC
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Give it extra damage of a different type
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Give non-lair monsters lair actions, and give monsters with lair actions an even stronger lair action they can use when below half-health. Same with legendary actions
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Look at older DnD editions and see if the monster or any similar monsters have extra abilities you can add
Edit: I should have specified that these are in ascending levels of difficulty for the DM, but are also more interesting
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Rules option for DnD 5E, specifically for legendary and mythical monsters that tend to be the ones with the most HP:
'Attacks from legendary or mythical monsters hit automatically if they require an attack roll and the effects of the attack would not give the target a condition. Legendary resistances of monsters can only be used against effects that can be assigned to the spell schools abjuration, illusion, transformation or enchantment. Otherwise, monsters can still use their Legendary Resistance to pass saving throws against any effect that would give the monster one or more conditions. In case of doubt, the DM decides. After a monster has used Legendary Resistance, its movement rate is halved until the end of its next turn. The damage caused by the monster's attacks that require attack rolls is also halved until the end of the monster's next turn after using Legendary Resistance.
(These rules can ensure that battles are both shorter and more exciting due to the higher damage dealt by both sides. The battles also become more dangerous, making PCs think twice about taking the risk. Creativity is encouraged when considering alternative strategies for conflict resolution. Both ensure that there will be fewer battles overall, which remain the most time-consuming scenes in the game. The increased risk also makes combat itself more creative when searching for ways to damage the enemy or use the environment for a tactical advantage. It also encourages the player characters to improve their supply of healing options, e.g. through the help of NPCs that can cast healing spells.)'
Scribbled together based on this post and its comments as well as some additional ideas I've had.
EDIT: Fixed something that got lost in automatic translation.