Battle of Floor 0507

The Battle of Floor 0507 was a skirmish between the Twelfth Doctor and the residents of Floor 0507 against the Cybermen invading from Floor 1056 on a Mondasian colony ship. Initially ruled by, the Cybermen turned on him when the Doctor rewrote their definition of humanity, leading to the group fleeing to the upper floor while the Cybermen prepared to conquer the entire ship.

The Cybermen held a significant advantage as they were further away from a black hole, meaning years for them was mere days for the Doctor and the others, allowing them more preparation time.

The skirmish was eventually ended when the Doctor, having had Nardole evacuate the majority of the residents to floor 0502, used his sonic screwdriver to ignite the floor, destroying all Cybermen present at the cost of forcing him to regenerate. (TV: The Doctor Falls)

Origins
Due to the colony ship being sucked into the orbit of s black hole, the Skelton crew on board went to floor 1056 to reverse the thrusters. However, the time dilation meant they aged much faster, several generations soon bring spawned. At some point, the Master crashed his TARDIS here and took control, eventually steering the residents down a path to convert the residents into cybernetic humanoids, and eventually a complete Cyberman. (TV: World Enough and Time)

The battle
The initial wave of Cybermen arrived, marching towards the town. However, they were met by a girl, who tossed an apple at them. Nardole, using his computer, ignited the fuel line beneath the platoon, blowing them up. The Master and Missy manoeuvred through the forest to the lift, witnessing the explosions on the distance, avoiding the Cybermen. Nardole proceeded to do this for the rest of the Cybermen, the house remaining safe, the Cybermen soon retreating. Understanding they had little time, the Doctor downloaded Nardole's software into his sonic screwdriver and (after a long argument) convinced Nardole to go with the evacuating children to protect them. Bill also opted to stay with the Doctor, wishing to die defending the children rather than continue living as a Cyberman.

By morning. The second wave arrived, the Doctor and Bill each charging into opposite ends of the forest, fighting of various types of Cybermen. As the Doctor did so, he shouted out the numerous occasions he had bested them, destroying numerous models of them. Eventually, he was surrounded and struck down by one Cyberman's laser beam. Wearily declaring he was still the Doctor, the Cyberman rebuked him and fired again. As his body attempted to regenerate, the Doctor ignited the entire floor, destroying all of the Cybermen and mortally wounding him in the process. (TV: The Doctor Falls)