Medrash tanchuma parshas teruma, siman 6 brings rebbe yehudah saying that it was a one-horned, large animal with 6 colors (the baal haturim writes that tachash is gematria “שש גונא”, which means 6 colors), according to rebbe nechemia it existed bederech neis for one time just to make the yerios (curtains) of the mishkan.
In shabboa 28a-b there’s a discussion regarding if the tachash was kosher, and if it was a chaya or behema; some hold that it’s a unique creature which is neither chaya nor behema.
Rav hirsch writes that the shoresh of the word tachash is חש, that it was able to run very fast