Fermion ~Mirai kara no Houmonsha~

The future isn't so bright. Pollution has severely weakened Earth and all of it's children, including humankind. Human DNA is too weak to reproduce itself and scientists are desperately trying to revive the human DNA. But every attempt fails, even the desperate attempt to fuse Human and Animal DNA turns out to create mutants that run amok.
Everything seems hopeless. But suddenly, scientists detect a space-time displacement, a gap in time. The gap will hold for a couple of days, and during which people may be sent through time.
Your mission as a Half-Human, Half-Feline, mutant-hunter Conny, is to back in time to the present (the late 20th century) and recover samples of healthy human DNA.

[From Anime Densetsu]