# Time Series Stationary but Variance Increases

I am somewhat a beginner to time series, so please bear with me. I was taught in class that when you difference a series too much times, the variance will increase, but I am also taught that I should difference the series at lag 1 until the mean of the series on the plot is a horizontal line. Before anyone asks, my data is not seasonal, and I have already Box-Cox transformed it. The series at this point does NOT have constant variance, but the scope of the course does not cover transformations to make variance constant, so that's all I can do in terms of transformations.

Then, I differenced my series once at lag 1 and got an increasing mean line in the plot, so I differenced again at lag 1. This time, I got an almost horizontal line, but my variance more than doubled the variance of differencing only once. What's more important: almost 0 mean or lower variance? Also, is there anything else I can try?