Since the online play for this is a wasteland, you're really only going to get this by setting up with a boosting partner. Here are some suggestions to shave off some of the per-game time to speed up the boosting.
1) I set my boosting sessions for two sets of 10, one set for the first boosting partner, then one set for the second. Partner A gets 10 wins in a row, then B does as well. This helps others out by getting the 10-in-a-row achievement. and breaks up the game into blocks of 10. Boosting 20 games in this way takes 40-50 minutes.
2) As the winning player, be sure to get three correct in a row to get another bonus card. Bonus cards play "faster" than other cards because there is no puzzle to solve, only an effect to be applied. Bonus cards are also very beneficial (see 3), Depending on what my hand looks like, I typically swap out a yellow card for the bonus card (see 4). Missing puzzles also gets you a card to replace, which adds time to the game.
3) As winning player, be sure to use your bonus cards. Bonus cards have ten effects, and two of those are to remove cards from that player's hand, and one is to play another card which speeds the end of the match. It might not seem like much, but shaving 20-40 seconds off of several games adds up over time. My typical use is to play out my hand strategically to get a second bonus card, then play both bonus cards on the chance that they will clear my hand.
4) If you can help it, don't play any yellow cards. These are observational puzzles and require you to watch an animation before you answer. As the winning player I would avoid these cards and try to get them at the "top" of my hand. Then, if I could get the "cards -1" or "cards -2", those would be the cards removed. Again, this might not seem like much, but shaving seconds off per game over 100-200 games (depending on how you are boosting) adds up over time.
5) As losing player, hit a button as soon as the puzzle comes up. If you aren't playing yellow cards, most puzzles should allow for an immediate answer. You can try to choose the wrong answers, but the questions should bear out that you get 1/2 - 3/4 of them wrong immediately. So long as the winning player is answering puzzles correctly, there should be no issue of accidentally winning.
6) As losing player, don't play any bonus cards. Two card effects add cards to the other player's hand, and this prolongs the game.
At 100 2-3 minute games, this is a minimum of 3.5-5 hours for the achievement, and you can double that if you're trading wins with a boosting partner. Perhaps not the most tedious slog toward an achievement, but it's up there.