DOOM + DOOM II

The easiest level to do this is in DOOM II on MAP32: Grosse. With this map, you will have access to a Plasma Gun, and the invulnerability sphere, both within close proximity to one another. Additionally, you can do this on the easiest difficulty: I'm Too Young To Die.

The trick to getting this achievement is both utilizing the Plasma Gun and abusing the Quick Save feature. Hit the Cyberdemon with some plasma shots, then Quick Save, wash, rinse, and repeat until you kill him. Reload that save right before you land the killing blow, switch to the pistol, and then take him out. Once you kill him, the achievement will pop immediately. You don't have to exit the level for it to unlock.

Here's a quick video guide by Xendemo with all of the secrets if you're struggling to find them yourself:

Can be easily done on Doom 1, E2M8: Tower of Babel lots of room and rocket ammo takes about 50 rocket hits to kill the Cyberdemon.