This is the first quest you receive after meeting the Girl who forgot her name. She is only seen after you save Cornelia from the Goblin attacks and return to Nine Wood Hills.
Any stacks can be used since the soldier has no elemental strengths or weaknesses. What I did was go back to the watch towers after the goblin invasion and caught a Black Nakk and one of almost every type of goblin. Here are the stacks I used:
Stack #1 – Jiant, Red Cap, Black Nakk Stack #2 – Jiant, Floating Eye, Sylph
Battle vs Bahamution Soldier (+ 2 Goblins)
HP – 2000
Size – Large
Loot – Phoenix Down
HP – 466
Size – Medium
Loot – Potion / Eye Drops
Elemental – +25 Fire / -25 Water / +25 Earth / -25 Light
Start by getting rid of the goblins. The soldier does not call any more, and you can dispatch them with Stack #2’s wind attacks. Since the soldier has no elemental weaknesses, you can use any attacks you want, but neutral damage attacks worked the best for me. Stack #1 is good for this, but Stack #2 is useful as well.