You absolutely need to have Black Magic in this fight, so get those Wisdom Earrings on Seth, and if you have any other Black Magic items, put them on Tolten and Sed. Then, each turn, blast the Dock Crane with one of your -a elemental spells. The more magic damage you inflict on it, the more the Charged Power bar in the corner of the screen will fill. When it fills completely, the Magic Beast will be given a final blow, despite how much health he may have. If you have three casters damaging the crane each turn, you can have the battle finished in three or four rounds easy; and in that time the Magic Beast will not be a threat at all. He'll get off a few Ground Strikes and Sonic Quakes, but neither are of any real danger. They'll do a few hundred damage at most even less to Sed, in the back row. If you don't have three casters you can also use elemental bombs (Flara, Aquara etc.) Sed is perfect for this since he can use double item.
Now if you have less than three casters, you may be forced to endure Flare Core (you'll know it's coming because it takes him three turns to cast it. Now that one's a biggie. When he's about to cast it have everyone Defend. Even with Defend, your front row will take 450-650 damage, but you should live. Just make sure to heal before and after if you are forced to suffer a Flare Core. The battle is perfectly winnable with just one caster, but as mentioned, it's easier with three. So search your inventory. You have to have something that allows you to cast magic.
NOTE: If you had Seth equip the Wisdom Earrings immediately after acquiring them she should learn the skill long before this battle, so you just need to give them to Tolten. Sed doesn't need magic because his rifle allows him to attack targets others can't reach. Also, I highly recommend you steal the Crystal Fragment from the Magic Beast because it didn't drop for me. ~Nemesis55444