I was trying to figure out the same thing and made this in Model Builder.
I am not good with scripting at all and new to model building but this was pretty easy to make and worth the effort.
Open model builder and select
INSERT > Iterators > feature selection. Use the input to be your polygon shapefile that contains the 30 different polygons; hopefully they are classified differently with an attribute like name. Select the
Group by fields drop down and put the name of the attribute you want to display for each individual rasters you are going to create.
Click ok, then in the Arctoolbox go to
data management > raster > raster processing > Clip and just drag that tool box into your model builder window. Double click the Clip icon and input the raster you want to use. Select your output folder, then (this is the tricky part) to ensure you get 30 individual raster images type in the name
%value%.tif at the end of your path location for the output.
Model > Validate entire Model, then of course
run entire model. It will take a while to proccess that many rasters but will certainly save time.
Last thing to change the spatial reference system click
Model > Model Properties > Check Output Coordinates > Values and browse to the one you want.