Necron

Necron is the Final Boss of Final Fantasy IX. He appears after Zidane defeats Trance Kuja, and represents death itself. Necron's ultimate goal is to reduce everything to nothingness. Since the game's main theme is life, he came in as the opposite of that.

Interestingly, he does have many links to Final Fantasy V. His appearance and name are both heavily reminiscent of the boss Necrophobe, and he uses Exdeath's Grand Cross attack. Moreover, as elaborated below, he may have originated as a tree, as Exdeath did.

Necron has the distinction of being able to perform three actions per turn, putting the party at a major disadvantage, especially if he casts Grand Cross, since Neutron Ring follows immediately after.

Battle
This is it, your final boss, strictly speaking he isn't as powerful as Ozma but still it should not be underestimated. Necron has plethora of Magic spells, each one stronger as he cast. His Firaga, Blizzaga, and Thundaga hits around 1500+ damage on all your characters. Aside from that, his can also cast Holy and Flare, which hits around 3000 in one character.

He'll also support buff himself with Protect and Shell, and will cast Curaga to heal up to 2500+ should he feel threatened. Like most final bosses, his "Shockwave" attack brings one character to 1 HP. Necron himself, has a few tricks of his own as well, his Neutron Star, hits around 4000+ to all your characters and finally, his most devastating attack, Grand Cross. Grand Cross functions similiar to Malboro's bad breath, only it inflicts every status ailments in the game, including Heat/Freeze.

Before fighting Necron, you'll have the opportunity to check your equipment one last time. It is highly recommended that every of your characters has Clear Head, Body temp, Antibody, and Jelly abilities to block some of Grand Cross's negative effects, such as Petrify, Confuse etc. You can also equip some other supportive abilities, like HP+, Auto-Regen, Auto-Haste to increase your advantages.

It is advised that you equip the "Bird Killer" and "MP attack" abilities to increase your damage inflict to Necron. Try not to use elemental Magics to strike Necron, unless it is supportive ones, Freya's Dragon Crest and Steiner's Climhazzard should be your powerhouse attacker. Just heal often and beware of Necron's attacks and you should be fine. Don't hesitate to let loose Elixirs, this is your final battle.

Enjoy the ending, you deserve it.

Speculation
When Garland is telling Zidane about the plan to restore Terra in Pandemonium Zidane comments on how they beat the monster (Soulcage) that breathes the mist (stagnant souls of the people of Gaia). Garland then tells him that what they saw was just the material form, or the back door, of the Iifa Tree. The true purpose of the Iifa Tree is Soul Divider i.e. the true form is Necron. Necron (in The Hill of Despair) receives the souls of Gaia and instead of them letting them go back into the Lifestream of the Planet to continue the Cycle of Souls he hoards them away and replaces them with the souls of Terra. Therefore the Cycle of Souls on Gaia will, after a few thousand years, be completely replaced with those of Terra. The purpose of Soulcage was to expel the now stagnant souls of Gaia back onto the planet but as nothing more than waste.

However, Garland, as he had done with Kuja, gave Necron a will which meant Necron was able to observe Kuja and make his own decisions. Because Kuja went to so many lengths in order to gain power and then decide to destroy everything by destroying the Crystal, Necron theorised that the only purpose of life was to die. Kuja had just killed the gang with his Ultima spell (and half killed himself in the process) when Necron realised this. He allowed the gang's souls to enter the Hill of Despair so he could explain his theory and thus prove it right by destroying the Crystal which would then result in the Zero World. This is a world in which there is nothing, no life, no death, no souls, and no memories.

When Necron was defeated he said "I am eternal" and "As long as there is life and death". There has been much debate amongst Final Fantasy fans as to what this means as this tend to deny what we know about Necron and suggests that he doesn't die. Necron took his theory to be his new identity. This is much like the Devil case. It is often wondered that without the idea of the Devil there would be no evil in the world because there would be no notion for which it has derived meaning. Necron had seen himself as the idea of the end of everything (the Zero World) and that he (the idea) would never die as long as there was the means of turning everything to the Zero World.