Tetra Sylphid has high evasion, attack type, and elemental resistances, but it's weak to Ice, and no magic resist. Status resistances are also quite high, so it's not a reliable option. It can also use a physical and magic shield skill, having a unit that can deal with shields may help.
The fight starts with Tetra Sylphid by itself, but wind elementals will soon spawn as reinforcements. It shows up 2 at a time, appearing at the outer circle of the main area in the center.
Wind elementals have decent HP and dangerously high MAG for a small enemy. They will be spamming a lot of wind magic, so it's recommended to bring a magic tank and try to increase magic resistances.
If you want to go with a magic dps route, a unit that can deal unresisted damage is someone that can deal ice magic damage.
Mediena has Blizzard spells, and LB reduces ice resist even more. Works best if you have a mono ice team.
Chel is a green mage unit that can use Imperil to reduce all elemental resistance. This really helps if you are using other elemental damage dealers.
Yuna also has green mage, but as a subjob. The imperil can really help, but she's a strong support to provide heals and revives as well.
Both Shiva and Fenrir have wind killers to help deal damage. Glacial and Golem can work too.
There will be a lot of wind magic attacks being spammed from Tetra Sylphid or the Wind Elementals. It's recommended to bring a magic tank along like Rain, but ice units will naturally have some wind resistance already, so going with a mono-ice team with no magic tank might still be alright.
Since you need to get a 3 chain to complete one of the missions to get the esper awakening material, it can help if you bring units that have multiple hit counts so you can clear it in one attempt. Otherwise, a mono element team is fine too.
Tidus can complete the mission easily by using his LB, while Luartha or Lu'Cia can use Quadruple shot. You may need high accuracy if you want to get all hits to connect on Tetra Sylphid, so it's easier to use multi hit moves on the wind elementals instead.
Tetra Sylphid Stats & Resistances
Max Level Stats
CT Change Nullified, Accuracy Up, Evasion Up, HP Debuff Res+999%