I know that here, people love very long and detailed answers, but I apologize I can't afford it. Here is my two cents:
You could take a look at the dungeons boss encounters in MMORPGs. Since the developpers make a lot of research in order to make the fight challenging, and yet feasible by a well balanced team, I think there is a lot of inspiration to take there, and there is even inspiration to take on the design of some packs of mobs along the way to the boss.
Among the tricks that they love using, there are often:
enrage timer: You have to kill the boss within 6min or so, in DnD it would be maybe 20 rounds before the goblin reinforcement arrive.
other timer: it can be regular events like the spawn of a new monster every 5 rounds and when there are 3 of them, they fuse to something very strong, or a periodic electric arc which will damage every adventurer who is less than 3m away from the others, etc.
order to kill: this is something they love setting up. For example if you kill the baby bear first, its mother will go berserk. Or you can have one of the foes among those that adventurers use to take down in the last that get a little stronger every two rounds, for example a mechanical golem that does nothing at the start because it needs some time to have all its weapon loaded
divide in two groups: Sometimes there are two twin bosses that need to be taken down almost at the same time unless you don't want them to super-berserk, but you can't fight both at the same place because they are stronger when they are together
puzzle: That last one is the deadlier, this is when there are events to trigger while fighting. For example the adventurers just reached the demon lord nest and they activated an ancient artifact to drain its energy and make it weaker so that they could match it. But the demon minions try to deactivate the artifact so they have to run the around the room and fight same, push the correct buttons and fight the boss at the same time. Or you can have a boss that needs to be taken alternatively to an ice lake and to a lava cascade.
take the max to hell: sometime when a mob has very low hp, it just kamikazes and explode dealing a lot of damage to everybody 30ft around.
The common point in all those mechanisms is that the adventurers need to carefully gather available info beforehand to have the data that will help them know how to fight, and to intelligently adapt during the fight to any occurring event.
You said that your group is used to take out the clerics and spell-caster first. Make them be the girlfriends of the fighter classes, and give those a permanent enrage buff whenever their girlfriend is dead, and next time the adventurers might think twice before applying this strategy.
Here is it. I don't pretend giving such detailed and informed answer some will probably give you, but I hope this will help ;)