Quick weapons checklist against those types:
Dragon: Dragoon Spear, Dragon Whip, Artemis Arrows
Reptile: Ice Rod
Spirit: Legend Sword, Light Sword, Excalibur, Crystal Sword, Silver Sword, Silver Staff, Silver Knife, Silver Hammer, Avenger Sword, White Spear, White Arrows, Artemis Bow
Giant: Ogre Axe, Poison Axe, Charm Claw, Charm Arrows, Drain Sword, Drain Spear
Undead: Legend Sword, Light Sword, Excalibur, Crystal Sword, White Spear, White Arrows
Mage: Mute Knife, Mute Arrows, Elven Bow, Silence Staff, Rune Axe
Mech: Thunder Claw, Thunder Arrows, Wooden Hammer, Silver Hammer, Earth Hammer
Flan: Drain Sword, Drain Spear
Sound about right?