You know, for a franchise as well known as Prince of Persia, I know nearly nothing about him. I know you've expressed wanting him in Smash before, but outside of acrobatics, a water sword and reversing time, what would he bring to the table moveset wise?
The prince is a sword fighter who fights with a dagger and can dual wield scimitars. He's capable of reversing time to a certain point. My idea on how to execute this in smash is to make it his up b recovery move, however the prince can only travel backwards in time depending on how many sands of time he has, it's a resource he has in the games that restricts how far he can go back and if it runs out then he can't time travel. He can regain the sands as the battle goes on and he inflicts and receives damage. I also believe the sands of time shouldn't put the prince in freefall, instead he has the opportunity to double jump from his reversed time or strike. If the prince returns back in time to a point where the opponent is exactly in then it would deal massive damage to the opponent, making his time manipulation not just a defensive option but also an offensive option, a high risk but high reward move.
The acrobatics he has would make his aerial acceleration very high among the cast which enables him to move faster in the air, likewise his jumps would be higher than average and he is able to wall jump.
His side special would be his dual wielding scimitar combo. It's similair to Marth's dancing blade where the prince has many options to strike up or down or forward. It seems simple, but that's because I have an idea to incorporate it with the down special.
The down special would be the prince's dark prince transformation. For the sake of balance this transformation would rely on the sands of time as well, if the sands run out then the transformation runs out. In compensation the dark prince transformation would allow him to deal more damage in his normals and aerials. The main change from this is that the side special would change from the dual scimitars to the daggertail chain whip, a much far reaching attack than the dual scimitars. If you played the God of War games then it's a bit similair to Kratos' chains. The Dark Prince transformation may be strong, but it uses the sands of time as resources which means if it runs out then recovering will be difficult, knowing when to use the transformation and when to turn it off will be important to take care of your sand.
For the neutral special we are going to use one of the djinn powers. The Prince will use ice blast, a move that creates a wave of ice traveling forward on the ground which damages enemies. The move would be able to carry the opponents with them like Greninja's water shuriken.
I tried my best to give the Prince a faithful moveset that at the same time fits with Smash's mechanics. I hope this helped visualize how the Prince would function in Smash.