Moon Lord

The Moon Lord is a Hardmode, post-Plantera boss that spawns after all four Lunar Events have been defeated. It is referred to as Terraria's "final boss". It has been confirmed by Cenx on a stream, that this is supposed to be Cthulhu's brother. (citation needed)

Parts
You must kill the hands and the heads before the core is opened and is available for the player to hit. You must kill all 4 of his body parts (consisting of his Hands, Head and Core) to kill him.

Tips

 * One should be wary of his mouth, as it will attach a tentacle to the player and pull multiple kill-able essence-like monsters out of the player. If not killed by the time they reach the mouth, the Moon Lord's Head is healed for 1000 health for each of them.
 * If one teleports to the spawn point in the middle of the fight, the Moon Lord will not despawn. Actually, he is pretty slow, so you could go back for healing whenever you are going to die, heal with the Nurse, return to the fight and carry him away from the spawn point. This technique can be repeated indefinitely.
 * Another workable method is to get into a high area, use the Phantasm to shoot upwards, and let the phantom arrows eat away at his mouth. This method also works with the Core.

Strategies:

 * Ride back and forth on a long bumper track and pelt him with bullets as a strategy. Also, put heart statues on their as a way to heal, as the moon lord can take away large amounts of health.

Trivia

 * Despite a mid-development comment by Cenx that this would not be the case, the Moon Lord resembles common depictions of Cthulhu, a creature first imagined by H. P. Lovecraft in his story, The Call of Cthulhu. It also fires "True Eyes of Cthulhu". This is partially a nod to broad fan speculation prior to the release of 1.3 that Cthulhu would be the final Terraria boss, which arose in part due to an early concept design floated by the development team.
 * This boss had originally been planned to be the moon itself descending on the world, however Cenx later stated this plan had been abandoned in favor of a different concept that was not revealed at the time. The new concept presumably became the Lunar Events and Moon Lord. The old concept may have been inspired by The Legend of Zelda: Majora's Mask, Final Fantasy VII, or the film Armageddon.
 * The Moon Lord shares similarities to a Tenome, a man-like creature with its eyes not in its face, but in the palm of its hands.
 * In a live stream, Cenx stated that the moon lord is Cthulu's brother.