A fight against Atma Weapon in a low-level, natural-magic challenge, which means magic can only be earned by leveling up (no espers), so you won't get much more than fire and cure.

The video's description contains the strategy the guy used, but I won't copy it here because it's so fucking long. I highly recommend you read it though.

Some info on it:

-It's done on an emulator. Save states are used, not during boss fights, but mostly to avoid leveling up;

-Atma Weapon has 24k HP and the FIGHT command does less than 100 damage;

-You must be really lucky to win this battle because he likes to target everyone in your party;

-Gau pwns. A lot.