Plot multiple variables of a 1-Dimensional xarray DataSet
So, you have one DataSet with two climatologies? And if you run data.clim1 or data.clim1 in the console, you see the the data sets and your climatologies are different? (Just to make sure, that you do not plot the same thing over each other.)
You should be able to plot them with:

import matplotlib.pyplot as plt 
plt.figure() 
data.clim1.plot() 
data.clim2.plot()

Hope that works. :)
Out of meterological data with 3 dimensions (lat, lon and time) I selected a subset and aggregated values of two different timespans/years into monthly means.
So at the end I have a DataSet where the dimension are the months (1-12) and there are two variables... Mean Values of timespan 1 and Mean Values of timespan 2.
Now I just want to plot these two variables on a simple Line chart to compare them. I already spent hours and days to find any advice on this, but it seems, that xarray isn't made for plotting multiple variables over each other? (Can't find anything useful for this)