In Final Fantasy IX all enemies can be defeated by a level 1 party, provided you have the right abilities (and a bit of luck).
With that said, I'm going to answer based on what Necron's damage output is, and what you can do to counter it:
- Firaga / Blizzaga / Thundaga
- Deals Fire / Ice / Thunder damage
- Blue Shockwave
- Puts a single party member at 1 HP
- Grand Cross
- Inflicts Beserk, Doom, Petrify, Stop, Freeze, Heat, Confuse, Poison, Trouble, Silence, Zombie, Darkness, Instant Death, Mini, Sleep and also reduces HP to 1-10
- Meteor / Flare / Neutron Ring
- Deals random / heavy / ludicrous non-elemental damage
- Curaga / Shell / Protect
- Heals / Resistance to Magic / Resistance to Physical
If possible, equip resistances against the most dangerous preventable status effects (Stop, Freeze/Heat, Confuse, Petrify)
- Clear Headed, Body Temp, Antibody, Locomotion & Jelly
This will prevent Grand Cross from completely handicapping your party. It's also not a bad idea to equip items that absorb/resist Holy and resist Elemental Damage:
- Resists Holy (Chimera Armlet, Ribbon, Pearl Rouge)
- Absorbs Holy (Pumice Piece)
- Resists Elemental Damage ( Ribbon, Protect Ring)
It's not a bad idea to equip Bird Killer, MP Attack and Auto-Regen
If you brought Freya, make sure to use the Jump Command and Rei's Wind, in order to regen your party, and at the same time avoid Necron's attacks. If you maxed out Dragon Crest, then use it instead for that cheeky 9999. If your party is low on MP, she can also use White Draw.
Amarant should be used as a supportive character. Everyone should have Auto-Life / Regen. Especially if he trances, his Monk Auto-Life is especially useful (so maybe you could put him near trance before the battle). Chakra is also useful if you brought an heavy MP consumer (Steiner, Dagger, Vivi)
Quina is lovely. White Wind helps you keep your party healthy, Angel Snack can be used to save your party if Grand Cross was used and if you maxed up Frog Drop, once again, that cheeky 9999.
Eiko is... situational. During Trance she has the double White Magic, which means you can use Curaga Twice. That's good, but since Necron can one shot sometimes, it won't be too helpful. Phoenix however, is great since you can ressurect all of your party. Bonus points if you equip a Phoenix Pinion on her, which has a small chance of ressurecting your whole party if all of you are KO'ed. You can also use Holy since Necron is weak vs Holy damage.
Dagger packs some good damage. Heal if needed, otherwise use your Summons to inflict damage. Ark is really good, especially if in Trance.
Zidane. Useless, unless you use one of two cheeses. Either have him be a super HP tank, and use sacrifice to heal others (and auto-life/heal Zidane) or use maxed out Thievery for that cheeky 9999 damage.
Steiner. Shock deals Physical damage. It's also his most reliable way to do 9999 damage. Although if you've leveled him enough his basic Attack (with MP-Power) can do 9999, especially with Excalibur II. He's also fairly tanky.
Vivi. Doomsday. Why would you use a spell that does Shadow Damage to not only your enemies but also your team? Well, first of all, it's his most damaging ability. Secondly, if you equip both pumice pieces and have the others use Elemental Resistances such as Protect Ring (50% elemental) + Dragon Wrist/Demon Vest (50% Shadow) or just an egoist's armlet (100% Shadow). If you equip all of your team with Absorb/Resist, Doomsday not only deals ludicrous damage, but also heals two of your party members.
Pick four and just use them to the best you can. Although be sure to pick something balanced. Essentially make sure you have at least someone that does (at least near) 9999 damage, someone who can revive/auto-life your teammates (Eiko,Dagger, Amarant, Quina) and someone who can reliably keep your team healthy (Vivi, Eiko, Dagger, Quina, Amarant - to an extent)