Necron can be an absolute pain the first time you face him (as a number of members have posted here requesting help fighting him in the past), but with themagic of a cut and paste from my reply to a simillar earlier thread (found at
Thread 18600 ):
Necron can be a proverbial pain-in-the-rear the first time you encounter him, (especially if your party is at a low level), but once you know how to handle him, he is a walk in the park. Firstly, I wouldn't attempt to battle him at a level lower than 40 (which was the average level my party was at the first time I attempted the final battle.), as he'll cut you to ribbons otherwise.
Secondly, make sure you've equipped everyone with all status-protecting abilities as it's the status effects Necron uses which wreak havoc with your party's health. Thirdly, having Auto-Regen equipped is invaluable, as you don't have to worry so much about healing yourself constantly.
Equip everyone with their most powerful weapons (Zidane with the Ultima Weapon, Steiner with Ragnarok or, if you have it, Excalibur II, Vivi with the Mace of Zeus etc) and have your mages know their most powerful spells (Holy, Ark, Madeen, Flare, Doomsday etc). Protecting yourself against elemental spells would also be a wise move.
As for the party to use, although you don't have to include Zidane in the final battle, I normally include him anyway, especially if he's equipped with the Ultima Weapon, as his final Dyne Trance attack Grand Lethal is deadly against Necron.
For the remaining three characters, I normally use Steiner (equipped with the Ragnarok), Vivi (with the Mace of Zeus) and either Eiko or Garnet, depending on what mood I'm in. Either one works well, although Garnet is probably better as her summon spells are stronger than Eiko's, and with Auto-Regen equipped, you have less a need for a White Mage than you do a Summoner. But it's up to you.
In battle, have Zidane attack physically (don't bother stealing as all Necron has is an Elixir), Steiner alternating between using his Shock sword attack and Doomsday Sword/Flare Sword, Vivi casting Flare like there's no tommorrow, and Garnet summoning Ark and Bahamut, healing the party if neccessary (casting Shell and Protect is wise too).
Necron starts out using Kuja's Flare Star attack, which can really hurt you if you're not careful, as well as a nasty attack called Neutron Ring which drops a character's HP down to 1 instantly. This is where Auto-Regen really comes into play. Having Garnet summon Ark while equipped with Auto-Regen ensures that while the summon animation is playing out (assuming she has the Boost ability equipped) your HP is still recovering, and as Ark is a very long animation, even if it was 1HP at the start your HP will be fully restored by the end of the attack, meaning all you have to do is sit back and watch your HP climb!
Necron also uses several souped-up elemental spells like Thundaga, Firaga and Blizzaga, but protecting yourself against these elements makes the attacks useless. The only attack of Necron you really have to watch out for is Grand Cross.
Grand Cross does no physical damage, but instead afflicts your party with four or five random and very nasty negative status effects. Some you can protect against, like Poison, Petrify and Darkness, but some you can't. Mini is annoying, but the real deadly ones are Zombie (especially with Auto-Regen equipped), Stop and Doom. And although it's rare, it is a very unlucky occurance to have all four characters suffer Instant Death (it has happened to me once.).
Have your characters immeidately remove the status effects with Remedies and abilities such as Esuna, then continue laying down the smack on Necron (by now you should be Tranced, so have Zidane finish off Necron with Grand Lethal and Vivi casting Double Flare. Believe me, by that point, Necron won't last long under that onslaught.) Just keep a cool head, and go into the battle properly prepared, and you'll win through!
Finally, as far as ethers go, defeating Hades in Memoria opens up his Synthesis Shop which allows you to synth ethers. So I strongly suggest you get a healthy supply before facing Necron, as nothing is worse than running low on MP.