I found this awhile back (no clue where, it's been awhile) and consult it when I need to spice up combat:
Defend the Innocent: The enemies aren't focused on the party, they're focused on a defenseless third party that the party needs to intervene and protect.
Stop the Ritual: The party has X turns to stop A Bad Thing from happening.
Achilles' Heel: The enemies are nearly impervious to conventional tactics except for a specific, crippling weakness that the party can exploit.
By The Power of Greyskull: The battle has some kind of power-up that the party can leverage to make an unwinnable fight winnable. Maybe the enemies have powerful, enchanted weapons in their armory and the party can steal them and use them for themselves, allowing you to throw more powerful enemies that the party shouldn't be able to fight at their current level. Maybe there's a magical wellspring that allows the spellcasters to regenerate spell slots, allowing them to cast their highest level spells more times than normal.
(Don't) Kick the Dog: A sympathetic character is fighting for the enemy, maybe mind controlled, maybe it's a misunderstanding, maybe the party just doesn't want to hurt this character, and the party needs to find a non-violent way to take them out of the fight, while they have no problems attacking the party. Crowd control is the key to this battle.
The Floor is Lava: Safe ground to stand on is ever-changing and dangerous. Maybe the ceiling of the ruined temple is collapsing, and each turn some rubble falls on a chunk of the battlefield, with only a round of warning before it does. This forces players who may be content to try and hold a position to move, potentially taking opportunity attacks or losing advantageous positioning.
Hold the Line: The battle is a test of endurance, the party has to survive X rounds against a seemingly overwhelming force before the tides of battle turn in their favor. The more avenues the players have to hold, the more they'll be stretched thin.
They Live: Enemies rise from the dead, have a second wind, or tap into some source of rejuvenation once defeated, and must be defeated again, this time with extra abilities.
Mêlée à Trois: A battle between 3+ equally antagonistic parties where the motivations for everyone involved is "the enemy of my enemy is also my enemy". See Jack Sparrow vs Will Turner vs Commodore Norrington from Pirates of the Caribbean.
Prove Your Worth: The battle includes a third party that is judging the players, or that they need to somehow influence to their side. This could be a gladiatorial combat where the group needs to win over the crowd, or maybe a subtrope of the Melee a Trois where the party has found themselves caught between enemies and a group of potential future allies, or maybe the maybe the party has stormed into the throne room to protect the king from his evil vizier and need to fend off the guards long enough to make their case. This is a roleplaying encounter mixed in with combat.
Hot Potato: The battle involves some kind of MacGuffin that can't be held by one person for too many turns and has to be traded off. Maybe the Orb of Baa'dGhai needs to be kept away from the enemies who want to summon the Dark Lord, but every round the players hold onto it they suffer a stacking debuff.
Reinforcements Incoming: Whether it's a Broodmother summoning more whelps, or battalions of soldiers arriving to the battlefield, this is a battle where the number of enemies can become overwhelming if not kept in check, and AOE attacks get an opportunity to shrine.
Enrage Timer: Each turn the enemies become stronger than the previous turn, so a fight that starts easy can quickly become overwhelming if the party tries to hoard their resources.
Romeo and Juliet: Enemies that are linked in some way and must be defeated within X rounds of each other or they will heal their counterpart.
Solve the Puzzle: The Ur-trope, there is some sort of puzzle that has to be solved before the battle can conclude. Maybe the party needs to find a group of hidden runes scattered in different corners of the battlefield to reveal the password to open the door that allows them to escape from a zombie horde.
VIP: A twist on the usual "defeat the boss and you win," reverse it and have a PC be the focus of a battle. Perhaps a barbarian warrior needs to prove that they’re tough enough to remain standing during a battle or a cleric of a light god is channeling the force of their god—the only thing enough to push back the darkness that threatens to consume the entire party. This can be a great way to put the spotlight on a specific character and allow them to shine (sometimes literally).
Capture the Flag: Instead of protecting a VIP, you’re fighting over an inanimate McGuffin, like a magic rune or bag of gold. Maybe once the party defeats the warlord, her underlings will try to grab the body and escape to resurrect her! Maybe the party’s goal is to steal a magic gem that’s guarded by a horde of eternally reanimating skeletons! Maybe the party has reached the end of the dungeon at the same time as a rival adventuring party, with both approaching the artifact contained within from opposite entrances to the final room! Now, in many Capture the Flag combats, battle may eventually degenerate back to a Team Deathmatch state, but simply having an objective can force battles to happen in circumstances that aren’t ideal to either side.
King of the Hill: Control a location. A ‘defensive’ King of the Hill might involve the PCs holding a specific door against enemies that want to burst in and assassinate whoever’s inside. An ‘offensive’ King of the Hill might involve the PCs trying to remain inside a ritual circle to disrupt the summoning of a dark god. The potential combinations are nearly endless.
Wave Defense: enemies don't all attack at once. The ‘alternate objective’ comes in with what I call the ‘Cross the Finish Line’ objective for enemies, which is a classic component of the Wave Defense in other game. Perhaps the party is defending a wall breach against attacking soldiers, or a holy gate against a horde of demons. The enemy can’t attack all at once due to the size of the gap, so they come in waves. Either it’s defeat a certain number of enemies or hold out for a certain amount of time (another alternate combat objective) in order to achieve victory.
Free for All: survival is focused on as the goal over body count. Perhaps this comes to a head with a battle between two factions? If either faction wins decisively, it makes the PCs lives much harder, so it falls to the PCs to ensure that any victory is pyrrhic. Perhaps an otherwise normal battle is interrupted by a wandering monster looking for an easy meal? Perhaps the Big Bad’s underling sees the climactic battle with the PCs as the perfect opportunity to betray their boss an eliminate both groups in one fell swoop? The Free for All is the perfect gift for the Diplomacy player in your game group—a challenge in which strategic thinking and diplomacy RP becomes just as essential to winning an encounter as optimal character design and tactical ability!