I think it's important to note that this achievement unlocks after the third time you fight and defeat Seymour Omnis. The third and last fight occurs when you're inside of Sin, near the end of the story. In this fight he's in front of 4 large discs and he will alternate different elemental attacks.
A cheap way to defeat himOne way to cheese this boss is to, like the other solution states, have all of your aeons in overdrive and use all of the overdrive attacks on Seymour. He has 80000 HP, so it should take most of that off, if not all. Seymour will no longer banish your aeons like in the previous fight, but he will just straight up kill them with multiple elemental attacks in a row. Pay attention to the discs behind him however. If you use your fire aeon for example and Seymour is planning to use fire attacks, the game will be stuck in an endless loop of the boss using firaga and your aeon absorbing it. Which leads me to think that Seymour will just keep attacking your aeon untill it dies. So you still have only one attack opportunity, like in the previous fights.
The cheapest way to defeat himThe cheapest way to defeat this boss, in a manner of speaking, is to summon the aeon Yojimbo in overdrive and pay him 50000 gil. He will one shot Seymour. The fight will last seconds.
Yojimbo will use an attack called Zanmato and use a dark looking blade dropping from the sky. It's unclear to me if he will do this everytime. It has to do with multiple factors. In my case I only used this aeon and his Zanmato attack once before, and I used him in overdrive against Seymour (by using Yuna's overdrive Grand Summon).
You can acquire Yojimbo in the Calm Lands on your playthrough if you have 200000 gil. See this achievement:
. If you missed him, you can go back after you have acquired the airship. You will get the airship after defeating Yunalesca.