The Cyberdemon is the first boss in the game. You fight him at the end of Mission 9 (Lazarus Labs). The fight is fairly easy. In the first phase, he mostly fires rockets which you can easily dodge by running in circles around him. When he uses the laser beam, just do a double jump to the side. A great weapon to down him quickly is the Heavy Assault Rifle with the Micro Missiles Mod. The missiles inflict a lot of damage quickly. When his health is depleted, he will respawn again with a full health bar. He will now be throwing some projectiles at you. Do one jump (not a double jump) to dodge them. There is also a checkpoint at the start of the second phase. When the second phase starts, immediately use the BFG to take away a lot of his health. Then, use the Heavy Assault Rifle or Plasma Rifle to kill him while dodging the projectiles.