Any process involved in the maturation of a precursor 5.8S ribosomal RNA (rRNA) molecule into a mature 5.8S rRNA molecule from the pre-rRNA molecule originally produced as a tetracistronic rRNA transcript that contains the Small Subunit (SSU) rRNA, the 8.8S rRNA, the 2S rRNA, and the Large Subunit (LSU) in that order from 5' to 3' along the primary transcript.