I like frankosity's ideas. It might be difficult to code it so cybie would intentionally smash walls, though. Maybe have him not use the rocket launcher until halfway in the game, or something like that? Could have a special entrance message on the floor when he first will use the rocket launcher. Nemesis actually used a rocket launcher in RE too, but not until later in the game.
It would be cool to have normal music until he enters at which point it switches to the cyberdemon walking track. If you do it where you have a headstart to finish the floor before he shows up, the mode would become similar in the timed aspect to angel of red alert, but handled in a way more like bubble bobble (anyone remember the white ghost that came after you when you spent too long on a floor?)
Actually, having a weaker (but still strong) cybie used for the levels other than the last would still work- the nemesis was easier earlier in the game than at the end in RE too.
Anyway, the example from resident evil need be no more than inspiration- the key is just having to deal with a cyberdemon of yet undetermined strength on each or many of the floors before the end. Something like running into him on every 5th floor could also potentially work.