Strategy A:
Scan Seymour with Sensor, then click on Seymour and see what order he casts his magic in. When you have learned this order, have Yuna cast the NulShields in the same order and he will never hit you. Every time you try to hit Seymour, one of his Guado Guards will jump in your way, and every time you hit a Guado Guard, he heals himself. To take out the two Guado Guards, use Rikku and your best hitter. Have Rikku to steal from one of the Guards and then have your best hitter attack that Guado Guard. You will get one Hi-Potion and the Guado Guard will not heal. When the Guards are dead and Seymour has exceeded his life, he summons Anima, an Aeon. You have seen Anima at the Blitzball Tournament. Use Yuna to summon the "????" Aeon, whom is Shiva. Use Boost for Shiva twice. This will put her into Overdrive. Before you use Diamond Dust (her Overdrive), heal yourself with Blizzard/Blizzara. Repeat this twice and Anima will die. Quickly dismiss Shiva. To defeat Seymour again, just cast the NulShields in the order of his magic and attack with your best hitters; or use Lulu, for Black Magic.
Strategy B:
Make sure that Yuna is in your attack party. Use her to cast NulBlaze, NulShock, NulFrost, and NulTide. Seymour and his Guado friends only use magic attacks and Confusion. Keep doing this until Yuna Reaches overdrive and use her "Grand Summon". You can use what ever Aeon you wish, but Ifrit is recommended. He will be charged with Overdrive because Yuna was, will kill the Guados. Seymour will summon Anima. You should use Boost once, take Anima's attack (which will only take away half of your life). After that, use Fira or Blizardra on yourself, depending on whether you chose Ifrit or Shiva to fight (elemental Aeons gain HP from their elemental attacks). Repeat this until you reach Overdrive and use your attacks. When Anima's Overdrive gauge is almost full, use Shield and his Overdrive will only take half of your life away. Repeat this until he dies. You will have to fight Seymour once again. Do what was you done before with the Nuls and use either magic or other attacks.
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Seymour 1 is considered an EXTREMELY hard fight for first time players. =)