To win a duel with Exodia, you need all 5 pieces of it in your hand at the same time: Right Arm, Right Leg, Left Arm, Left Leg, and Exoida the Forbidden One. Once you have all 5, you automatically win.
The Exodia deck is very easy to make and extremely overpowered. You can use this deck for all of the single-player battles, just not for online as it is deemed illegal in the game's rules for competitive games. I will list cards by the Card Shop's booster pack you can find them in. The number in the brackets is the cost per pack. The majority of these packs can be obtained in the first series, except Alexis Rhodes, which is at the start of GX. I recommended grinding the damage achievements first, and I will post my decks for that ASAP. Once you have done grinding (should be by the end of the first series) then use your coins to buy packs. You may have won some of these cards already.
Once you have these cards, your task is to draw as many cards as possible using the abilities on each card. I won almost every duel, some on turn 1. In the video below, I show some methods to obtain more cards. including destroying your own monsters. Use this technique when you only need one more card to win. I also show my deck. Grandpa Muto packs. (200).
- Right Arm of the Forbidden One x3
- Left Arm of the Forbidden One x3
- Right Leg of the Forbidden One x3
- Left Leg of the Forbidden One x3
- Exodia the Forbidden One x3
- Scapegoat. Try to chain this card for the 100 chains achievement.
- Pot of Duality x3
- Raigeki x2
- Graceful Charity x3
- Spirit of the Pot of Greed
- Backup Squad. This card breaks the AI. They won't attack your life points directly for some strange reason, even when they can win. Bakura packs. (400).
- Pot of Greed x3
- SanganMai Valentine packs. (400)
- Upstart Goblin x2Yugi packs. (400).
- Heart of the Underdog x2
- Gold Sarcophagus x2Alexis Rhodes packs. (400).
This is the first pack won in GX.
- Emissary of the Afterlife
- Swords of Revealing Light x2 Gong Strong packs. (400)
- This is pack is from the first few battles in ARC-V, so you can skip ahead and unlock that pack if you wish.
- Supply Squad. You should also get won after beating Bandit Keith in Challenge Mode. Beat him in Campaign > Yu-Gi-Oh! > Keith's Machinations to unlock him. This card is a luxury, don't worry too much about it.
Some of these cards are already part of the default stock you have.
You can find info on all cards here.