A Eukaryote is a complex cell with membrane-bound structures inside. If it is Heterotrophic, it gains its energy from organic carbon, and thus is not in the plant kingdom (plants are autotrophs, generating energy from sunlight and inorganic compounds).
In this case, since the cell is animal, the phylum choice is limited to water-based eukaryotes. Cells with tails are called Flagellates, and are often found in the kingdom Protista: these are both plant and animal. One of the most common cells of this type are the phylum Dinoflagellate, which are plant and animal cells living in water. Heterotrophic dinoflagellates would include microscopic plankton, which live and reproduce in the ocean, make their own energy from organic carbon compounds, and move with a tail-like structure.