The Beast Between existed before the Fantendoverse, and while it was being created he asked of Ektaz to leave a space outside of the universe, where he could continue his peaceful existence (this event also lead to the creation of the Darktendoverse, as Ektaz discovered universes could exist side-by-side).
Despite only briefly appearing, the Beast Between is the major focus of the game, as the game's conflict is caused by Jirea attempting to create a hole in the Fantendoverse through which he could learn of the Beast Between's knowledge.
In Days of Shattering, the Beast Between makes a brief appearance in the prologue, stating that it was "no dream" that Leila was experiencing. It is unknown at the moment what he's talking about.
The Beast Between was given a actual design in Fantendo Smash Bros. Shattered by Exotoro. As he resides in between universes, the idea is that he has multiple shadows that float around his consciousness. His face consists of something similar to a beast, but with his upper mouth and jaw switched. We can also see something resembling a TV test pattern, perhaps showing that he is no longer observing the universes.