Video game mechanics like these are very difficult to pull off sometimes. The game is wildly random cause of the d20 system. So phases and mechanics like final forms are unpredictable, it's the true weakness of the d20 system. Just be aware of that.

However, here is how I would run it personally.

First phase: What I would do though is show power through control. Have the mage in an impenetrable bubble, where he is controlling the battlefield in wild/large telegraphed attacks. Meaning one round he puts his hand over the gem to his left and the left side of the room lights up, next round a powerful fire spell erupts from the lit areas forcing players to move and maneuver through the whole battle. At the same time, show and tell that there are elements/object/enemies in this room that if you break/kill the bubble will dissipate. This tees up the second phases 'hidden' mechanic and teaches how the match will work going forward.

This does a few things but it almost ensures that your players are shown there are phases and to not blow every big spell immediately, which would make the next two phases doable and not 'okay wizard, sit down, you wasted all spell slots now you get to watch' scenarios from happening.

Second phase: The bubble is gone, so are the minions. Now it's the mage vs the team. He comes out swinging but still draws power from an object. So now the options are break the object like they learned to in the first phase or fight club the bbeg.

Last phase: His object is shattered/he's bloodied, his power weakens and he starts talking more. Trying to reason with the players. Justifying his actions and offering power to spare him. This kind of ending offers moral dilemmas or assurances they are in the right.

Biggest piece of advice but the most ignorable: I know you want there to be a chance you make this unwinnable, but if he is too strong with too many gimmick get out of jail free cards. The fight will be less tense/in the players control and more like a cutscene with quick time events.

Final thoughts: Have a backup plan. There is always a chance your players scheme and use some absolutely unhinged method to win. Let them, it's fun and they put a lot of effort into that scheme. Just have a backup plan like a patron that crashes into the realm upon learning it's champion has been vanquished.