The Hybrid

The Hybrid was a Gallifreyan legend telling of a creature thought to be crossbred from two warrior races - the Time Lords and the Daleks - according to prophecies from the Matrix. Rassilon was searching for information about the Hybrid as according to the legend it would stand over the ruins of Gallifrey. (TV: Hell Bent)

References

Davros attempted to transform some of his Daleks into Time Lord hybrids, intending to fulfil an ancient Gallifreyan prophecy which warned of a Dalek-Time Lord Hybrid that would conquer Gallifrey. (TV: The Witch's Familiar) However, the Twelfth Doctor later claimed the Daleks would never allow anything to be half-Dalek and that the hybrid of Time Lord prophecy was "Me". (TV: Heaven Sent) He later shared this theory with Ashildr, at which point she countered with the theory that either he singly was the Hybrid. Alternatively, she suggested that if the Hybrid could be interpreted as being more than one being, then the Hybrid could refer to the pair of the Doctor and his companion Clara Oswald. Another theory was that the hybrid might be the Doctor and the Master's relationship. (TV: Hell Bent, Face the Raven)

Possible Interpretations of the Hybrid

In all possible theories of its identity, the Hybrid refers to itself as "Me." This leads to several possible interpretations as to who it is based on the theories mentioned above. The three most prominent candidates for being the Hybrid are the Doctor, Ashildr, and the Doctor and Clara put together.

Ashildr

When Ashildr died after helping him and her village fend off the Mire, the Doctor resurrected her using a Mire medical kit. The result was Ashildr becoming immortal and losing the "ability" to die. (TV: The Girl Who Died) The next time the Doctor encountered her, Ashildr was calling herself "me", after living through centuries of losing everyone she ever loved. From lovers to children, she continually lost people she cared about until she became callous and uncaring towards others and bitter towards the Doctor for condemning her to such a lonely existence. She told the Doctor that the name she called herself now was "Me", since there was no one else to call her "Ashildr", and that because she would be the only constant in her life. (TV: The Woman Who Lived)

The Doctor

While the death of his companion Clara Oswald was still impending, the Doctor threatened Ashildr with exposure to the world if she did not do anything to save her. When Ashildr pointed out that the Doctor would never do such a thing, the Doctor's chilling reply was "The Doctor is no longer here, you are stuck with me now!" It's possible that the moment Clara died was the moment the Doctor became the Hybrid. (TV: Face the Raven) As stated above, when the Doctor emerged from his confession dial onto Gallifrey, he explained that the Hybrid couldn't be half-Time Lord-half-Dalek as the Daleks would never allow a half-Dalek being to exist given their ideas on racial purity. In keeping with the theory, the Doctor - donning his sonic sunglasses - disclosed that the Hybrid was "Me." (TV: Heaven Sent, Hell Bent)

The Doctor and Another Person

When the Doctor met Ashildr again at the end of the universe in the ruins of the Cloisters, she told him her theory that the Hybrid was not one person but two, the second being either Clara or the Master. The Doctor dismissed this theory along with another theory she had where the Doctor ran away from Gallifrey because he was afraid of himself. (TV: Hell Bent)