There are 3 ways to get this achievement:
The fastest is obviously to spend money and buy all of the masters. With enough money, this can be done in just a few matches. Just make a deck, switch to the master you want, and enter any online Battle.
The second fastest way, but takes some work and knowledge is to use draft mode. Every draft you participate in gives you a random choice of 3 masters. That's the easy part. Then you have to build a good enough deck to win 1 match before you lose 3, picking 1 of a random selection of 3 cards for each card in your deck.
The final way is to build a solid constructed deck and beat a Battle with your given master and each of the 2 free weekly rotation masters. Doing it this way only will take a minimum of 4 weeks depending on the rotation schedules.