As a follow-up to the optical spectroscopic campaign aimed at achieving completeness in the Third Catalog of Hard Fermi-LAT Sources (3FHL), we present here the results of a sample of 28 blazars of an uncertain type observed using the 4m telescope at Cerro Tololo Inter-American Observatory in Chile. Out of these 28 sources, we find that 25 are BL Lacertae objects (BL Lacs) and 3 are flat-spectrum radio quasars (FSRQs). We measure redshifts or lower limits for 16 of these blazars, and it is observed that the 12 remaining blazars have featureless optical spectra. These results are part of a more extended optical spectroscopy follow-up campaign for 3FHL blazars, where, until now, 51 blazars of an uncertain type have been classified into BL Lac and FSRQ categories. Furthermore, this campaign has resulted in redshift measurements and lower limits for 15 of these sources. Our results contribute toward attaining a complete sample of blazars above 10 GeV, which then will be crucial in extending our knowledge on blazar emission mechanisms and the extragalactic background light.