This achievement requires you to completely finish this game. In order to do that, there are several things you have to do. They are:
1. Play through and complete the single player campaign.
2. Play through and complete the co-op player campaign.
3. Complete all the puzzles.
4. Unlock every add-on card for every deck.
Add on content, if you downloaded it, will add a couple more decks, along with a couple more cards for all the previous decks. It also will add a couple more puzzles for you to do, along with an addition to the single player campaign AND a second (4 matches) co-op campaign.
Most of the puzzles are fairly straight forward, but for detailed videos, go look at the solutions posted for the Puzzling Master and Magic: The Puzzling achievements.
Unlocking the cards for all the decks is as described before, you can have a friend quit out, or rig a custom game with the CPU and smash your way to victory. This portion is by far the most time consuming.
The single player campaign is fairly straight forward. In general, use the green deck to smash everything until you unlock the black deck, then use that to finish the single player.
The co-op campaign, however, is more frustrating. Generally, it would be best to have your friend come over and play with you, but not all of us have that luxury (friends that play, or even friends that come over). I honestly didn't even START this portion until a couple days ago, and of course it is easier to do when your deck is maxed out. This is the method I've been using to make slow yet steady progress:
I used a second account, which only had access to the solid green deck, and not maxed out. With my main account, I just have been trying to choose the best deck to counter the two decks I'm playing against. For example, when I'm versing the Black deck, I either go with the Blue (counter spells) or Artifact (prevents terror's and fear's from running the game). Playing against the Scales of fury deck, I would use the Elf (overpower with trample and numbers) or the Fire deck (haste and direct damage) to just blitz attack them. Using the green deck to augment my army, such as Blanchwood Armor and Giant Growth to help my creatures survive or rule. Best part about the co-op, you can share abilities (like putting blanchwood armor on the Flameblast Dragon, etc).
So far, up to the time I'm writing this, I am only missing 2 battles (expansion co-op) from obtaining this achievement (98% complete), which I plan on finishing tonight.
Also of note: If you have the expansion pack, and have NOT completed the co-op campaign, you will notice that the final match in the co-op campaign (the first one) changes. It is no longer between Tezzerete and Tezzerete, but between Tezzerete and the guy with the dragon deck (forget the name right now). But when you do defeat them, it still will pop the achievement for completing the co-op campaign, and when you check the achievement in your list, the text description will reflect the player swap.
Edit: It is now the next day, and I was able to manage to beat the final two battles, but some advice for the final battle: I gave up using other decks and went with my solid white deck. Reason? The computer has to be cheating. They will get EXACTLY what they need to defeat you almost every single time. Both decks you are versing have 3+ Terror's (by my count) in them, which they LOVE to use in BULK to destroy EVERYTHING on the field, they also have Terminates, they both have a Platinum Angel, the dragons, artifacts, and strong black and red spells make fighting these decks a pain in the behind.
Artifact deck loves to boost the Glaze Fiend, the other deck just screws you up. They have a creature that takes your creatures when they die unless you pay 3 life to prevent it. Serious pain in the @$$
My game of goof.. They have 9 life, I have 4, they only had 1 blocker (5/5 Flameblast Dragon), I had 3 creatures, 2/2 bears, 2/2 civic elf, 11/11 regenerating troll (blanchwood armor, holy strength), all their creatures are tapped (deathtouch owl, glaze fiend, and something else i forget) except the dragon they just summoned. Accidentally placed second blanchwood on troll instead of other creature. Of course i lost next turn.
Winning Game.. no white creatures on field (got terrorized to hell again) Regen troll with blanchwood, kept killing things on attack, out comes Platinum Angel, they have just ground walking creatures and no flying (well, the ones they had i pacified) played my +3/+3 +Flying until end of turn on troll, made them negative life, then reached into my white hand and pulled out my...
Mass Calcify FTW
Quite easily the hardest match up in the entire game.
With the addition of an additional expansion pack (expansion 2), more cards (3) are added to each previous deck, and 3 more decks with 15 cards unlockable apiece dropped my completion percentage down into the 70%'s. More grinding out wins against a handicapped CPU or more time your friends need to quit games to boost you to full 100% completion.
Achievement suggestion: attain your "Plainswalker" achievement before downloading expansion content. Will reduce the amount of time you need to grind out wins. Of course, then you wouldn't have to unlock the additional cards, which would be sinful, as most are awesome.