Not fast but a way to get this without purchasing any plants.
After growing a lot of plants over time in a single pot I decided to toss all of the plants and the game asked me if I wanted to start a new pot. I said sure and it gave me a new pot with 10 plants. I let those plants grow for a couple of weeks (I waited until some of them had flowered) and then tossed them all. At that point the game gave me another pot with 10 plants. I just repeated this until the achievement popped. I wasn't in a hurry so it took a couple of months but I didn't have to worry about buying any plants either.