Starting from scratch, if you've unlocked most of the main achievements in the game, you'll probably be at around 2500 matches. Remember, this is only from a few puzzles. Just keep going for the other achievements and this will come naturally. I'd suggest getting the difficulty based achievements done first. Once those are all done, you'll probably be at around 3000-4000 matches. From there, just keep playing the game normally. Just come back daily and make progress towards completing one of the puzzle packs. By the time you complete the 100 puzzles in a pack, you should be very close to this one.
All matches including those made in daily challenges count. Even if you don’t finish a puzzle the matches still count. So if you’re working on a daily challenge achievement, you’ll be making progress towards this one. Also, even if you undo and redo a move, each subsequent attempt of a move will count towards the achievement.
Boosting/grinding: To boost specifically this achievement, I'd recommend medium puzzles. They have a large number of pieces and few blockages. Easy puzzles have fewer pieces, but can be completed quicker. Hard and expert puzzles have more pieces but are more prone to blockages. So medium puzzles are perfect for boosting this achievement. Just pick your favorite medium puzzle and complete it 10 to 15 times a day. If you want a rapid completion, I’d recommend the first puzzle which looks like a key. This one is easy to grind as it has a good layout. Blockages are rare here. It gives you 24 matches per run. This is great to use for your last couple hundred matches. Puzzle 11 is also a good one since the pieces are well spread out, meaning you’ll always be able to complete it. Another way to rapidly grind this is to memorize a certain section. Find an easy path to take. Then, simply make those matches, undo back to the start match again and repeat.