I accomplished this fairly easily in the Yu-Gi-Oh! Campaign and "The Ultimate Great Moth" Duel. Using the story deck, the cards are present for summoning Gaia the Dragon Champion. You need the following 3 cards:
-Gaia the Fierce Knight
-Curse of Dragon
-Polymerization
What made this duel fairly easy is that as long as you can get one monster to keep Weevil under control, you can bide your time until you get the set above. Since this duel is relatively early in the Campaign, it's not too difficult either. The only annoyance and worry I had in the duel was his usage of Swords of Revealing Light. Thought he might have summoned something stronger during those lulls, but he never did. The monster I had out to control while waiting was Kaiser/Dark Magician powered up with the Unicorn Horn. Either was powerful enough to guide me through.
Once you have this, just wait till you get what you need. I can't say for sure, but based on the Special Summon stack, you should have 2 Poly, 2 Gaia, and 2 Curse of Dragons in the deck.
After getting the 3 cards, activate Polymerization, select Gaia and Curse and then summon Gaia the Dragon Champion. Following this, the achievement unlocks.