To unlock all of the challenges you need to first complete every duel in the each single player campaign and the reverse duels as well.
After that the quickest way to beat each challenge deck, that I've found so far, is an Exodia deck. I modeled my Exodia deck after the Exodia cheat deck you get when you beat Seeker. I changed a couple cards around since I didn't own a few, but it still revolves around the concept of milling through your deck as fast as possible. With the deck I had I was able to routinely win matches in 3-4 turns with practically no effort and it's possible to win before your opponent even has a turn. Choosing to go first after the rock-paper-scissors is also helpful to getting those 1 turn wins. I was able to get through 10 or so challenge duels in about 20 minutes as opposed to a 3-5 duels with my Fire Fist deck. And the best thing about this deck, minimal attention and skill is required. Honestly, I didn't need to pay attention to nearly any of my opponents plays; just focused entirely on my cards.
Here's my deck list:
Exodia the Forbidden One x3
Right Leg of the Forbidden One x3
Left Leg of the Forbidden One x3
Right Arm of the Forbidden One x3
Left Arm of the Forbidden One x3
Emissary of the Afterlife x2
Pot of Greed x3
Swords of Revealing Light x3
Pot of Duality x3
One Day of Peace x3
Graceful Charity x3
Dark World Dealings x2
Heart of the Underdog x2 (I'd remove these if you have more Upstart Goblin cards, only owned one)
Upstart Goblin x1
Dark Hole x1
Gagaga Cowboy x2 (not really needed, but can help in a pinch)
I'll be modifying it too as I get more and better cards.