Unlocking the Alchemist Room in Monster Ball requires that you have 1250 dosh and "activate" a locked door near the spawn location. Once you have 1250 dosh (I was able to do this solo after 2 waves on normal difficulty), head over to the door and press B to unlock it. Once the door opens, the achievement will pop. I made a video to show the location and how to get to the door from the initial spawn.
Note: I had already unlocked the achievement before making this video. The achievement should pop as soon as the door opens.
Edit: According to user CrosscutSlinky, if you're having trouble unlocking this achievement, "Try going to the official club page for the game, that's how I got the achievement to unlock for me."