Phantoms (ファントム, Phantom) are recurring enemies in the Zelda series.
Phantoms first originated in The Legend of Zelda: Phantom Hourglass, as guardians of a temple that Link must visit at various points throughout the game. They are shown to be indestructible for a large portion of Phantom Hourglass, and getting attacked by one would result in Link being sent to the beginning of the temple. Phantoms in this game come in three variations, each with their own abilities.
They reappear in The Legend of Zelda: Spirit Tracks with the same function, although this time they guard the Tower of Spirits and now come in four variations. After Link and Zelda head to the Tower of Spirits, they are ambushed by Chancellor Cole and his apprentice Byrne who take away her body with plans to resurrect the evil Malladus on atop of the Tower of Spirits, which broke apart during the ecounter. Later on, during Link's first encounter with a Phantom where he was helpless, Zelda's soul proceeded to rush to his aid and accidentally entered the Phantom though its back, resulting in her finding out that she can possess the Phantoms while inside one. From that point onwards, Link & Zelda made use of the unique abilities of each Phantom type in order to progress though the Tower of Spirits with each following visit on their quest to restore the Spirit Tracks and tower, and to reach the tower's top.
At the end of their journey before the final battle, Link & Zelda were able to free Zelda's original body from Malladus' possession. As Zelda has control of the Phantom from SSB4 onwards, the move is most likely referencing Spirit Tracks.
In Super Smash Bros. 4
A phantom appears as part of Phantom Slash, which replaces Zelda's ability to transform into Sheik as the 3DS hardware could not handle the transformation sequence. Rather than possessing the Phantom physically like in Spirit Tracks, Zelda simply commands it to attack beside her.
The Phantom appears as a trophy exclusivly in the 3DS version.
In Super Smash Bros. Ultimate
The Phantom reappears as part of Zelda's Phantom Slash.
The Phantom appears as a Spirit, which can be enhanced into the Zelda from Spirit Tracks.