Boss Fights tend to come in one of two flavors in the world of videogames: stat checks and puzzles. In a stat check boss fight there is nothing particularly special to the mechanics of fighting the boss. It is just a question of if you can avoid or tank the boss's damage while doing enough damage to get through the boss's defenses before you lose.
In an RPG like Final Fantasy or Dragon Age this means healing your people, potentially positioning them well, and managing your resources to do your damage and keep your people alive through the fight. In a more action game like Devil May Cry this involves the player having to avoid the damage combos of the boss while dishing out their own damage combos in the windows of opportunity.
In a puzzle boss fight, there is more to the fight than just doing raw damage. The boss is a puzzle requiring specific actions at specific times in order to beat it. This is made harder in that you have to survive the boss's damage while doing this.
It goes without saying that of the two most boss encounters in Table Top RPGs fall into the 'stat check' category.
This is not surprising. RPGs like D&D and Pathfinder have Monster Manuals full of Challenge Ratings to tell you at about what level the PCs will have the stats to beat the monster. Some monsters have tricks to them - using bludgeoning against skeletons in D&D is often a valuable strategy. There is also synergy bonus and tactics that the PCs can use to maximize their output while minimizing the damage coming their way.
But it is rare you have to do specific actions to unlock a window of opportunity against a boss. Even simpler mechanics like "you need to bait the boss into charging into a wall to stun it" don't happen often. So why is it?
I think it is because there are a number of challenges to doing it that makes it hard to execute, and also very, very dangerous. Like campaign ending dangerous.
Problem 1: Turn Based Slows Things Down
Actions like the aforementioned 'bait it into ramming a wall to stun it' can be awkward in a turn based game. How long is it stunned for? What happens if a PC does damage or something that could distract the boss after a PC successfully tries to bait it? How do you keep track of if the bait is done correctly or locks things in?
Problem 2: Communicating a Puzzle vs. Giving Away the Puzzle
The whole point of a puzzle is that the PCs have to figure it out. However, in a fight that can be hard to do. You need to communicate that there is a puzzle mechanic in play, and where that puzzle mechanic might be without just giving away the puzzle. Sure, you can reward creativity and help move things along, but it is still a fine line to walk and very hard to set up.
Problem 3: Combat Can Be Frustrating. Puzzles Can Be Frustrating. Both Together?
Let's be honest. Tensions get high when the boss is dishing out 1/2 a tank's HP in damage every attack. And when tensions get high, people aren't exactly thinking their most creative thoughts. At the same time, puzzles can frustrate people as it is hard to perfectly communicate the idea in your head in such a way that people can solve the problem, and when they think they have it but their ideas keep failing? Well you start getting frustrated. Combine those and you have a recipe that can leave people feeling they're wasting a LOT of their time all the while dealing with the negative aspects of combat at the same time.
Problem 4: If They Don't Solve The Puzzle, A TPK Is Likely
The end result of not out-statting a boss is often a TPK, but it is a TPK that can be 'controlled for' by making sure the PCs stats and the boss's stats are not too out of line with each other. However, when the vulnerability window for a boss is locked behind a puzzle, that skews the relation. ANd if the PCs can't solve the puzzle...they very likely could die. Combined with Problem 3 and this is a recipe for an end of campaign with a lot of flustered and frustrated PCs.
All that said, I think one can be done. I mean, technically I've done one before. In a Superhero game I had a villain named 'Tank Man' who simply could not be hurt by the PCs. In fact, the first time they fought him, I gave them all a hero point after they all took a shot and said "you do not have enough damage to hurt him. You're going to have to find a non-attack option to deal with him."
The PCs never did, but being a super hero game they never died to it either. They did knock him out one time. The 6 PCs + 2 guest appearance PCs (friends who were visiting) all did a group attack where half of them rolled nat 20s, so I bent the rules and let their super attack knock him down...once.
The solution was to exhaust him, but as I said the PCs never figured it out in game. Still, it did work. They hated tank man IC, dreaded him showing up, but loved him OOC because he'd led to some memorable moments.
So it can work.
But if you want to do them, you need to keep those problems in mind - and your group. And you may have to flat out say "this isn't just a combat encounter."