You might try an Imhoff separation cone to try and settle out the heavier zooplankton. We have also used sieves with different sized mesh to separate small phytoplankton from larger zooplankton, but there will always be phytoplankton left behind stuck to the zooplankton.

You could also pick the zooplankton species that you want to do the stable isotopes on from the samples because different species will have somewhat different isotope values. That will give you isolated zooplankton from the phytoplankton. Sometimes you can grab a whole-water sample that isolates phytoplankton from zooplankton. Good luck!

After segregating through separate mesh sized nets, staining methods can distinguish between both types of phytoplankton